# 1 3 4 7 11

OEIS link Name First elements Short description A000002 Kolakoski sequence {1, 2, 2, 1, 1, 2, 1, 2, 2, 1, …} The

kaki langit
th term describes the length of the

horizon
th run A000010 Euler’s totient function

φ(n)
{1, 1, 2, 2, 4, 2, 6, 4, 6, 4, …}
φ(horizon)

is the number of positive integers not greater than

horizon

that are coprime with

n
. A000032 Lucas numbers

L(falak)
{2, 1, 3, 4, 7, 11, 18, 29, 47, 76, …}
L(tepi langit) =
L(t
− 1) +
L(n
− 2)

for

horizon
≥ 2
, with

L(0) = 2

and

L(1) = 1
. A000040 Prime numbers

p

t

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …} The prime numbers

p

lengkung langit

, with

n
≥ 1
. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A000041 Partition numbers

P

cakrawala

{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, …} The partition numbers, number of additive breakdowns of n. A000045 Fibonacci numbers

F(n)
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …}
F(n) =
F(n
− 1) +
F(n
− 2)

for

n
≥ 2
, with

F(0) = 0

and

F(1) = 1
. A000058 Sylvester’s sequence {2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, …}
a(falak
+ 1) =
a(horizon)⋅a(ufuk
− 1)⋅ ⋯ ⋅a(0) + 1 =
a(horizon)2

a(falak) + 1

for

cakrawala
≥ 1
, with

a(0) = 2
. A000073 Tribonacci numbers {0, 1, 1, 2, 4, 7, 13, 24, 44, 81, …}
Cakrawala(n) =
T(cakrawala
− 1) +
T(n
− 2) +
T(n
− 3)

for

cakrawala
≥ 3
, with

N(0) = 0 and
T(1) =
T(2) = 1
. A000079 Powers of 2 {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, …} Powers of 2: 2
ufuk

for
falak
≥ 0 A000105 Polyominoes {1, 1, 1, 2, 5, 12, 35, 108, 369, …} The number of free polyominoes with

lengkung langit

cells. A000108 Catalan numbers

C

n

{1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …}

${\displaystyle C_{n}={\frac {1}{n+1}}{2n \choose n}={\frac {(2n)!}{(n+1)!\,n!}}=\prod \limits _{k=2}^{n}{\frac {n+k}{k}},\quad n\geq 0.}$

C

n

=

1

n
+
1

(

2
n

n

)

=

(
2
n
)
!

(
kaki langit
+
1
)
!

n
!

=

k
=
2

ufuk

ufuk
+
k

k

,

n

0.

{\displaystyle C_{n}={\frac {1}{ufuk+1}}{2n \choose n}={\frac {(2n)!}{(lengkung langit+1)!\,n!}}=\prod \limits _{k=2}^{t}{\frac {ufuk+k}{k}},\quad t\geq 0.}

A000110 Bell numbers

B

n

{1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, …}
B

n

is the number of partitions of a set with

n

elements. A000111 Euler zigzag numbers

E

ufuk

{1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, …}
E

n

is the number of linear extensions of the “zig-zag” poset. A000124 Lazy caterer’s sequence {1, 2, 4, 7, 11, 16, 22, 29, 37, 46, …} The maximal number of pieces formed when slicing a pancake with

tepi langit

cuts. A000129 Pell numbers

P

n

{0, 1, 2, 5, 12, 29, 70, 169, 408, 985, …}
a(n) = 2a(n
− 1) +
a(n
− 2)

for

ufuk
≥ 2
, with

a(0) = 0,
a(1) = 1
. A000142 Factorials

n!
{1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, …}
n! = 1⋅2⋅3⋅4⋅ ⋯ ⋅n

for

n
≥ 1
, with
0! = 1
(empty product). A000166 Derangements {1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, …} Number of permutations of
horizon
elements with no fixed points. A000203 Divisor function

σ(kaki langit)
{1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, …}
σ(falak) :=
σ
1(n)

is the sum of divisors of a positive integer

n
. A000215 Fermat numbers

F

n

{3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, …}
F

ufuk

=
2

2

n

+ 1

for

horizon
≥ 0
. A000238 Polytrees {1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, …} Number of oriented trees with
falak
nodes. A000396 Perfect numbers {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, …}
ufuk

is equal to the sum

s(falak) =
σ(ufuk) −
n

of the proper divisors of

lengkung langit
. A000594 Ramanujan tau function {1,−24,252,−1472,4830,−6048,−16744,84480,−113643…} Values of the Ramanujan tau function,

τ(ufuk)

at
n
= 1, 2, 3, … A000793 Landau’s function {1, 1, 2, 3, 4, 6, 6, 12, 15, 20, …} The largest bestelan of permutation of

t

elements. A000930 Narayana’s cows {1, 1, 1, 2, 3, 4, 6, 9, 13, 19, …} The number of cows each year if each cow has one cow a year beginning its fourth year. A000931 Padovan sequence {1, 1, 1, 2, 2, 3, 4, 5, 7, 9, …}
P(tepi langit) =
P(horizon
− 2) +
P(kaki langit
− 3)

for

tepi langit
≥ 3
, with

P(0) =
P(1) =
P(2) = 1
. A000945 Euclid–Mullin sequence {2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, …}
a(1) = 2;
a(lengkung langit
+ 1)

is smallest prime factor of

a(1)
a(2)
⋯ a
(lengkung langit) + 1
. A000959 Lucky numbers {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, …} A natural number in a set that is filtered by a sieve. A000961 Prime powers {1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, …} Positive integer powers of prime numbers A000984 Central binomial coefficients {1, 2, 6, 20, 70, 252, 924, …}

${\displaystyle {2n \choose n}={\frac {(2n)!}{(n!)^{2}}}{\text{ for all }}n\geq 0}$

(

2
n

ufuk

)

=

(
2
falak
)
!

(
kaki langit
!

)

2

for all

n

0

{\displaystyle {2n \choose n}={\frac {(2n)!}{(cakrawala!)^{2}}}{\text{ for all }}kaki langit\geq 0}

, numbers in the center of even rows of Pascal’s triangle A001006 Motzkin numbers {1, 1, 2, 4, 9, 21, 51, 127, 323, 835, …} The number of ways of drawing any number of nonintersecting chords joining

cakrawala

(labeled) points on a circle. A001013 Jordan–Pólya numbers {1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64. …} Numbers that are the product of factorials. A001045 Jacobsthal numbers {0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, …}
a(n) =
a(n
− 1) + 2a(ufuk
− 2)

for

n
≥ 2
, with

a(0) = 0,
a(1) = 1
. A001065 Sum of proper divisors

s(n)
{0, 1, 1, 3, 1, 6, 1, 7, 4, 8, …}
s(n) =
σ(cakrawala) −
cakrawala

is the sum of the proper divisors of the positive integer

horizon
. A001190 Wedderburn–Etherington numbers {0, 1, 1, 1, 2, 3, 6, 11, 23, 46, …} The number of binary rooted trees (every node has out-degree 0 or 2) with

n

endpoints (and
2t
− 1

nodes in all). A001316 Gould’s sequence {1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, …} Number of odd entries in row
tepi langit
of Pascal’s triangle. A001358 Semiprimes {4, 6, 9, 10, 14, 15, 21, 22, 25, 26, …} Products of two primes, titinada necessarily distinct. A001462 Golomb sequence {1, 2, 2, 3, 3, 4, 4, 4, 5, 5, …}
a(n)

is the number of times

n

occurs, starting with

a(1) = 1
. A001608 Perrin numbers

P

n

{3, 0, 2, 3, 2, 5, 5, 7, 10, 12, …}
P(horizon) =
P(n−2) +
P(n−3)

for

n
≥ 3
, with

P(0) = 3,
P(1) = 0,
P(2) = 2
. A001855 Sorting number {0, 1, 3, 5, 8, 11, 14, 17, 21, 25, 29, 33, 37, 41, 45, 49 …} Used in the analysis of comparison sorts. A002064 Cullen numbers

C

tepi langit

{1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, …}
C

n

=
falak⋅2
n

+ 1
, with

kaki langit
≥ 0
. A002110 Primorials

p

horizon
#
{1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, …}
p

falak
#
, the product of the first

n

primes. A002182 Highly composite numbers {1, 2, 4, 6, 12, 24, 36, 48, 60, 120, …} A positive integer with more divisors than any smaller positive integer. A002201 Majikan highly composite numbers {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, …} A positive integer

falak

for which there is an

e
> 0

such that

d(tepi langit)

/

tepi langit

e

d(k)

/

k

e

for all

k
> 1
. A002378 Pronic numbers {0, 2, 6, 12, 20, 30, 42, 56, 72, 90, …}
a(n) = 2t(n) =
n(n
+ 1)
, with

t
≥ 0

where

t(n)

are the triangular numbers. A002559 Markov numbers {1, 2, 5, 13, 29, 34, 89, 169, 194, …} Positive integer solutions of

x
2
+
y
2
+
z
2
= 3xyz
. A002808 Composite numbers {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, …} The numbers

n

of the form

xy

for

x
> 1

and

y
> 1
. A002858 Ulam number {1, 2, 3, 4, 6, 8, 11, 13, 16, 18, …}
a(1) = 1;
a(2) = 2;

for

n
> 2,
a(ufuk)

is least number

>
a(tepi langit
− 1)

which is a unique sum of two distinct earlier terms; semiperfect. A002863 Prime knots {0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, …} The number of prime knots with
n
crossings. A002997 Carmichael numbers {561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, …} Composite numbers

lengkung langit

such that

a

n
− 1

≡ 1 (mod
n)

if

a

is coprime with

n
. A003261 Woodall numbers {1, 7, 23, 63, 159, 383, 895, 2047, 4607, …}
n⋅2
n

− 1
, with

horizon
≥ 1
. A003601 Arithmetic numbers {1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, …} An integer for which the average of its positive divisors is also an integer. A004490 Colossally abundant numbers {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, …} A number
horizon
is colossally abundant if there is an ε > 0 such that for all
k > 1,

${\displaystyle {\frac {\sigma (n)}{n^{1+\varepsilon }}}\geq {\frac {\sigma (k)}{k^{1+\varepsilon }}},}$

σ

(
n
)

n

1
+
ε

σ

(
k
)

k

1
+
ε

,

{\displaystyle {\frac {\sigma (falak)}{n^{1+\varepsilon }}}\geq {\frac {\sigma (k)}{k^{1+\varepsilon }}},}

where
σ
denotes the sum-of-divisors function.

A005044 Alcuin’s sequence {0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, …} Number of triangles with integer sides and perimeter

n
. A005100 Deficient numbers {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, …} Positive integers

t

such that

σ(horizon) < 2ufuk
. A005101 Abundant numbers {12, 18, 20, 24, 30, 36, 40, 42, 48, 54, …} Positive integers

tepi langit

such that

σ(n) > 2n
. A005114 Untouchable numbers {2, 5, 52, 88, 96, 120, 124, 146, 162, 188, …} Cannot be expressed as the sum of all the proper divisors of any positive integer. A005132 Recamán’s sequence {0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, …} “subtract if possible, otherwise add”:
a(0) = 0; for
n
> 0,
a(n) =
a(horizon
− 1) −
n
if that number is positive and not already in the sequence, otherwise
a(n) =
a(kaki langit
− 1) +
cakrawala, whether or not that number is already in the sequence. A005150 Look-and-say sequence {1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, …} A = ‘frequency’ followed by ‘digit’-indication. A005153 Practical numbers {1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40…} All smaller positive integers can be represented as sums of distinct factors of the number. A005165 Alternating factorial {1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, …} cakrawala! − (n−1)! + (n−2)! − … 1!. A005235 Fortunate numbers {3, 5, 7, 13, 23, 17, 19, 23, 37, 61, …} The smallest integer

m
> 1

such that

p

n
# +
m

is a prime number, where the primorial

p

lengkung langit
#

is the product of the first

n

prime numbers. A005835 Semiperfect numbers {6, 12, 18, 20, 24, 28, 30, 36, 40, 42, …} A natural number

ufuk

that is equal to the sum of all or some of its proper divisors. A006003 Magic constants {15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, …} Sum of numbers in any row, column, or diagonal of a magic square of bestelan

n
≥ 3
. A006037 Weird numbers {70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, …} A natural number that is abundant but not semiperfect. A006842 Farey sequence numerators {0, 1, 0, 1, 1, 0, 1, 1, 2, 1, …} A006843 Farey sequence denominators {1, 1, 1, 2, 1, 1, 3, 2, 3, 1, …} A006862 Euclid numbers {2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, …}
p

t
# + 1
, i.e.
1 +
product of first

n

consecutive primes. A006886 Kaprekar numbers {1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, …}
X
2
=
Ab

n

+
B
, where
0 <
B
<
b

n

and

X
=
A
+
B
. A007304 Sphenic numbers {30, 42, 66, 70, 78, 102, 105, 110, 114, 130, …} Products of 3 distinct primes. A007850 Giuga numbers {30, 858, 1722, 66198, 2214408306, …} Composite numbers so that for each of its distinct prime factors
p

i

we have

${\displaystyle p_{i}^{2}\,|\,(n-p_{i})}$

p

i

2

|

(
n

p

i

)

{\displaystyle p_{i}^{2}\,|\,(n-p_{i})}

. A007947 Radical of an integer {1, 2, 3, 2, 5, 6, 7, 2, 3, 10, …} The radical of a positive integer

ufuk

is the product of the distinct prime numbers dividing

t
. A010060 Thue–Morse sequence {0, 1, 1, 0, 1, 0, 0, 1, 1, 0, …} A014577 Regular paperfolding sequence {1, 1, 0, 1, 1, 0, 0, 1, 1, 1, …} At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. A016105 Blum integers {21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, …} Numbers of the form

pq

where
p
and
q
are distinct primes congruent to
3 (mod 4). A018226 Magic numbers {2, 8, 20, 28, 50, 82, 126, …} A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. A019279 Superperfect numbers {2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, …} Positive integers

falak

for which

σ
2(t) =
σ(σ(n)) = 2n.
A027641 Bernoulli numbers

B

n

{1, −1, 1, 0, −1, 0, 1, 0, −1, 0, 5, 0, −691, 0, 7, 0, −3617, 0, 43867, 0, …} A034897 Hyperperfect numbers {6, 21, 28, 301, 325, 496, 697, …}
k
-hyperperfect numbers, i.e.

tepi langit

for which the equality

n
= 1 +
k
(σ(n) −
falak
− 1)

holds. A052486 Achilles numbers {72, 108, 200, 288, 392, 432, 500, 648, 675, 800, …} Positive integers which are powerful but imperfect. A054377 Primary pseudoperfect numbers {2, 6, 42, 1806, 47058, 2214502422, 52495396602, …} Satisfies a certain Egyptian fraction. A059756 Erdős–Woods numbers {16, 22, 34, 36, 46, 56, 64, 66, 70, 76, 78, 86, 88, …} The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. A076336 Sierpinski numbers {78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, …} Odd

k

for which

{
k⋅2
ufuk

+ 1 :
n

${\displaystyle \mathbb {N} }$

N

{\displaystyle \mathbb {N} }

}

consists only of composite numbers. A076337 Riesel numbers {509203, 762701, 777149, 790841, 992077, …} Odd

k

for which

{
k⋅2
horizon

− 1 :
ufuk

${\displaystyle \mathbb {N} }$

N

{\displaystyle \mathbb {T} }

}

consists only of composite numbers. A086747 Baum–Sweet sequence {1, 1, 0, 1, 1, 0, 0, 1, 0, 1, …}
a(n) = 1

if the binary representation of

n

contains no block of consecutive zeros of odd length; otherwise

a(n) = 0
. A090822 Gijswijt’s sequence {1, 1, 2, 1, 1, 2, 2, 2, 3, 1, …} The

horizon
th term counts the maximal number of repeated blocks at the end of the subsequence from
1
to

n−1
A093112 Carol numbers {−1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, …}

${\displaystyle a(n)=(2^{n}-1)^{2}-2.}$

a
(
n
)
=
(

2

ufuk

1

)

2

2.

{\displaystyle a(kaki langit)=(2^{cakrawala}-1)^{2}-2.}

A094683 Juggler sequence {0, 1, 1, 5, 2, 11, 2, 18, 2, 27, …} If

t
≡ 0 (mod 2)

then

n

else
n
3/2
. A097942 Highly totient numbers {1, 2, 4, 8, 12, 24, 48, 72, 144, 240, …} Each number

k

on this list has more solutions to the equation

φ(x) =
k

than any preceding

k
. A122045 Euler numbers {1, 0, −1, 0, 5, 0, −61, 0, 1385, 0, …}

${\displaystyle {\frac {1}{\cosh t}}={\frac {2}{e^{t}+e^{-t}}}=\sum _{n=0}^{\infty }{\frac {E_{n}}{n!}}\cdot t^{n}.}$

1

cosh

t

=

2

e

t

+

e

t

=

n
=
0

E

n

n
!

n

n

.

{\displaystyle {\frac {1}{\cosh falak}}={\frac {2}{e^{falak}+e^{-t}}}=\sum _{n=0}^{\infty }{\frac {E_{n}}{n!}}\cdot ufuk^{falak}.}

A138591 Polite numbers {3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, …} A positive integer that can be written as the sum of two or more consecutive positive integers. A194472 Erdős–Nicolas numbers {24, 2022, 8190, 42336, 45864, 392448, 714240, 1571328, …} A number
n
such that there exists another number
m
and

${\displaystyle \sum _{d\mid n,\ d\leq m}\!d=n.}$

d

n
,

d

m

d
=
n
.

{\displaystyle \sum _{d\mid n,\ d\leq m}\!d=t.}

A337663 Solution to Stepping Stone Puzzle {1, 16, 28, 38, 49, 60 …} The maximal value

a(lengkung langit)

of the stepping stone puzzle

OEIS link Name First elements Short description A000027 Natural numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …} The natural numbers (positive integers)

falak

${\displaystyle \mathbb {N} }$

N

{\displaystyle \mathbb {N} }

. A000217 Triangular numbers

t(n)
{0, 1, 3, 6, 10, 15, 21, 28, 36, 45, …}
t(n) =
C(n
+ 1, 2) =

t(falak
+ 1)

/
2

= 1 + 2 + ⋯ +
n

for

ufuk
≥ 1
, with

t(0) = 0

(empty sum). A000290 Square numbers

n
2
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, …}
n
2
=
n
×
kaki langit
A000292 Tetrahedral numbers

T(horizon)
{0, 1, 4, 10, 20, 35, 56, 84, 120, 165, …}
T(n)

is the sum of the first

n

triangular numbers, with

T(0) = 0

(empty sum). A000330 Square pyramidal numbers {0, 1, 5, 14, 30, 55, 91, 140, 204, 285, …}

horizon(kaki langit
+ 1)(2lengkung langit
+ 1)

/
6

: The number of stacked spheres in a pyramid with a square base. A000578 Cube numbers

n
3
{0, 1, 8, 27, 64, 125, 216, 343, 512, 729, …}
lengkung langit
3
=
ufuk
×
ufuk
×
n
A000584 Fifth powers {0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, …}
horizon
5
A003154 Star numbers {1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, …} Skaki langit

= 6n(kaki langit
− 1) + 1. A007588 Stella octangula numbers {0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, …} Stella octangula numbers:

n(2n

2

− 1)
, with

horizon
≥ 0
.

OEIS link Name First elements Short description A000043 Mersenne prime exponents {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, …} Primes

p

such that
2
p

− 1

is prime. A000668 Mersenne primes {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, …} 2
p

− 1

is prime, where

p

is a prime. A000979 Wagstaff primes {3, 11, 43, 683, 2731, 43691, …} A prime number
p
of the form

${\displaystyle p={{2^{q}+1} \over 3}}$

p
=

2

q

+
1

3

{\displaystyle p={{2^{q}+1} \over 3}}

where
q
is an odd prime. A001220 Wieferich primes {1093, 3511} Primes

${\displaystyle p}$

p

{\displaystyle p}

satisfying
2
p−1

≡ 1 (mod
p
2)
. A005384 Sophie Germain primes {2, 3, 5, 11, 23, 29, 41, 53, 83, 89, …} A prime number

p

such that
2p
+ 1

is also prime. A007540 Wilson primes {5, 13, 563} Primes

${\displaystyle p}$

p

{\displaystyle p}

satisfying
(p−1)! ≡ −1 (mod
p
2)
. A007770 Happy numbers {1, 7, 10, 13, 19, 23, 28, 31, 32, 44, …} The numbers whose trajectory under iteration of sum of squares of digits map includes
1. A088054 Factorial primes {2, 3, 5, 7, 23, 719, 5039, 39916801, …} A prime number that is one less or one more than a factorial (all factorials > 1 are even). A088164 Wolstenholme primes {16843, 2124679} Primes

${\displaystyle p}$

p

{\displaystyle p}

satisfying

${\displaystyle {2p-1 \choose p-1}\equiv 1{\pmod {p^{4}}}}$

(

2
p

1

p

1

)

1

(
mod

p

4

)

{\displaystyle {2p-1 \choose p-1}\equiv 1{\pmod {p^{4}}}}

. A104272 Ramanujan primes {2, 11, 17, 29, 41, 47, 59, 67, …} The

horizon

th
Ramanujan prime is the least integer

R

n

for which

π(x) −
π(x/2) ≥
kaki langit
, for all

x

R

n

.

OEIS link Name First elements Short description A005224 Aronson’s sequence {1, 4, 11, 16, 24, 29, 33, 35, 39, 45, …} “falak” is the first, fourth, eleventh, … letter in this sentence, not counting spaces or commas. A002113 Palindromic numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121…} A number that remains the same when its digits are reversed. A003459 Permutable primes {2, 3, 5, 7, 11, 13, 17, 31, 37, 71, …} The numbers for which every permutation of digits is a prime. A005349 Harshad numbers in base 10 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, …} A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). A014080 Factorions {1, 2, 145, 40585, …} A natural number that equals the sum of the factorials of its decimal digits. A016114 Circular primes {2, 3, 5, 7, 11, 13, 17, 37, 79, 113, …} The numbers which remain prime under cyclic shifts of digits. A037274 Home prime {1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, …} For

n
≥ 2,
a(n)

horizon
, concatenate its prime factors (A037276) and repeat berayun-ayun a prime is reached;

a(horizon) = −1

if no prime is ever reached. A046075 Undulating numbers {101, 121, 131, 141, 151, 161, 171, 181, 191, 202, …} A number that has the digit form

ababab
. A046758 Equidigital numbers {1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, …} A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046760 Extravagant numbers {4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, …} A number that has fewer digits than the number of digits in its prime factorization (including exponents). A050278 Pandigital numbers {1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, …} Numbers containing the digits
0-9
such that each digit appears exactly once.

Source: https://en.wikipedia.org/wiki/List_of_integer_sequences

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