A111389 -id:A111389 - cp's OEIS frontend

A046063 Numbers k such that the k-th partition number A000041(k) is prime.

2, 3, 4, 5, 6, 13, 36, 77, 132, 157, 168, 186, 188, 212, 216, 302, 366, 417, 440, 491, 498, 525, 546, 658, 735, 753, 825, 841, 863, 1085, 1086, 1296, 1477, 1578, 1586, 1621, 1793, 2051, 2136, 2493, 2502, 2508, 2568, 2633, 2727, 2732, 2871, 2912, 3027, 3098, 3168, 3342, 3542, 3641, 4118

Offset: 1

Eric W. Weisstein

The corresponding primes are given in A049575. - Joerg Arndt, May 09 2013

Max Alekseyev, Table of n, a(n) for n = 1..4967 (contains all terms below 10^8)
Chris K. Caldwell, Top twenty prime partition numbers, The Prime Pages.
G. P. Michon, Table of partition function p(n) (n=0 through 4096)
G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), Volume 1(6) (2014), ISSN: 2349-8862.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.
Eric Weisstein's World of Mathematics, Partition Function P.
Eric Weisstein's World of Mathematics, Integer Sequence Primes.

Cf. A000041, A035359, A049575, A051143, A111036, A111045, A114165, A111389, A113499, A114166, A114167, A114168, A114169, A114170, A115214.

Select[ Range@3341, PrimeQ@ PartitionsP@# &] (* Robert G. Wilson v *)

for(n=0,10^5,my(p=numbpart(n));if(isprime(p),print1(n,", "))); \\ Joerg Arndt, May 09 2013

from sympy import isprime, npartitions
print([n for n in range(1, 5001) if isprime(npartitions(n))]) # Indranil Ghosh, Apr 10 2017

b-file extended by Max Alekseyev, Jul 07 2009, Jun 14 2011, Jan 08 2012, May 19 2014

A111036 Numbers n such that p(6n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

1, 6, 22, 28, 31, 36, 61, 83, 91, 181, 216, 263, 356, 417, 418, 428, 528, 557, 777, 1133, 1243, 1408, 2170, 2708, 3046, 3867, 5100, 5540, 5662, 7418, 9397, 12110, 12797, 14787, 16161, 16482, 18022, 19431, 19667, 21180, 22011, 22720, 23560, 27903

Offset: 1

Parthasarathy Nambi, Nov 11 2005

nonn

			If n=91 then p(6n) = 27833079238879849385687 (prime).

Max Alekseyev, Table of n, a(n) for n = 1..782

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[33333], PrimeQ[ PartitionsP[6# ]] &] (* Robert G. Wilson v *)

is(n)=isprime(numbpart(6*n)) \\ Charles R Greathouse IV, Feb 17 2017

a(10)-a(45) from Robert G. Wilson v, Nov 14 2005

A111045 Numbers n such that P(4n) is prime, where P(m) is the number of partitions of m.

Original entry on oeis.org

1, 9, 33, 42, 47, 53, 54, 110, 324, 534, 627, 642, 683, 728, 792, 1114, 2112, 2228, 2323, 2770, 3007, 3255, 3368, 3760, 4062, 4569, 6139, 7650, 7939, 8138, 8310, 8493, 8674, 9122, 9407, 10345, 11127, 13343, 14713, 15442, 15632, 16358, 16904, 18165, 19303

Offset: 1

Parthasarathy Nambi, Nov 11 2005

nonn

			If n=110 then P(4*n) = 74878248419470886233 (prime).

Max Alekseyev, Table of n, a(n) for n = 1..1271

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[19923], PrimeQ[ PartitionsP[4# ]] &] (* Robert G. Wilson v *)

is(n)=isprime(numbpart(4*n)) \\ Charles R Greathouse IV, Feb 17 2017

a(9)-a(37) from Robert G. Wilson v, Nov 14 2005

A114165 Numbers n such that p(2n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

1, 2, 3, 18, 66, 84, 93, 94, 106, 108, 151, 183, 220, 249, 273, 329, 543, 648, 789, 793, 1068, 1251, 1254, 1284, 1366, 1456, 1549, 1584, 1671, 1771, 2059, 2131, 2228, 2331, 2501, 3399, 3729, 4224, 4456, 4646, 4999, 5093, 5540, 6014, 6510, 6736, 7520, 8124

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

2n-th partition number (A000041(2n)) is prime.

Max Alekseyev, Table of n, a(n) for n = 1..2451

Cf. A000041, A046063, A068413, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[9137], PrimeQ[ PartitionsP[2# ]] &]

is(n)=isprime(numbpart(2*n)) \\ Charles R Greathouse IV, Feb 17 2017

A114166 Numbers n such that p(5n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

1, 88, 105, 147, 165, 217, 1481, 2216, 2579, 2604, 3008, 3658, 3694, 4329, 4353, 4447, 4534, 5074, 5793, 6120, 6578, 6648, 7861, 7994, 8276, 8851, 9421, 10371, 12350, 12359, 12389, 13010, 13345, 13479, 14532, 14727, 16461, 19313, 19466, 20354

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..1252

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[20780], PrimeQ[PartitionsP[5# ]] &]

is(n)=isprime(numbpart(5*n)) \\ Charles R Greathouse IV, Feb 17 2017

A114167 Numbers n such that p(7n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

11, 24, 75, 78, 94, 105, 155, 211, 293, 416, 506, 666, 1860, 3013, 3508, 3811, 4869, 5615, 5710, 8824, 8841, 8998, 10380, 11014, 11779, 13795, 14276, 15285, 18014, 19456, 19855, 22435, 23343, 23391, 26328, 30608, 31380, 32074, 32810, 33459

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..810

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[28571], PrimeQ[PartitionsP[7# ]] &]

is(n)=isprime(numbpart(7*n)) \\ Charles R Greathouse IV, Feb 17 2017

A114168 Numbers n such that p(8n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

21, 27, 55, 162, 267, 321, 364, 396, 557, 1056, 1114, 1385, 1684, 1880, 2031, 3825, 4069, 4155, 4337, 4561, 7721, 7816, 8179, 8452, 9962, 15885, 16871, 17024, 17040, 17670, 22186, 23037, 26782, 31307, 35364, 35442, 38430, 42307

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..630

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[25000], PrimeQ[PartitionsP[8# ]] &]

is(n)=isprime(numbpart(8*n)) \\ Charles R Greathouse IV, Feb 17 2017

A114169 Numbers n such that p(9n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

4, 24, 144, 277, 278, 303, 319, 352, 518, 2279, 2405, 2578, 3400, 3787, 4273, 4457, 7603, 9145, 9858, 10774, 10988, 11545, 12954, 14120, 14674, 17537, 18193, 18602, 18919, 21955, 29775, 30559, 31504, 34160, 35618, 35655

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..555

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

Select[ Range[22222], PrimeQ[PartitionsP[9# ]] &]

is(n)=isprime(numbpart(9*n)) \\ Charles R Greathouse IV, Feb 17 2017

A114170 Numbers n such that p(10n) is prime, where p(n) is the number of partitions of n.

Original entry on oeis.org

44, 1108, 1302, 1504, 1829, 1847, 2267, 2537, 3060, 3289, 3324, 3997, 4138, 6175, 6505, 7266, 9733, 10177, 11483, 12708, 12881, 13632, 14136, 14414, 15917, 16409, 17614, 19133, 19381, 21966, 22967, 30565, 30744, 31655, 33783

Offset: 1

Robert G. Wilson v, Nov 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..607

Cf. A000041, A046063, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170, A070177.

Select[ Range[20000], PrimeQ[PartitionsP[10# ]] &]

is(n)=isprime(numbpart(10*n)) \\ Charles R Greathouse IV, Feb 17 2017

A113499 Numbers n such that P(11*n) is prime where P(n) is the partition number.

Original entry on oeis.org

7, 12, 40, 75, 163, 228, 261, 288, 322, 331, 618, 678, 768, 926, 2990, 3821, 4852, 5726, 10802, 11710, 12006, 12635, 14470, 18097, 22156, 25776, 29142, 32692, 36965, 48830, 51821, 56433, 58008, 63757, 64433, 67545, 68391, 69850, 73723, 77498, 77770

Offset: 1

Parthasarathy Nambi, Jan 10 2006

nonn

n belongs to this sequence if and only if 11*n belongs to A046063.

			If n=163 then P(11*n) = 11820527237297139926370474832027317722017807 (prime).

Max Alekseyev, Table of n, a(n) for n = 1..467

Cf. A111036, A111045, A111389.

For[n = 1, n < 1000, n++, If[PrimeQ[PartitionsP[11*n]], If[ProvablePrimeQ[PartitionsP[11*n]], Print[n]]]] (* Stefan Steinerberger *)
Do[ If[ PrimeQ@ PartitionsP[11n], Print@n], {n, 3000}] (* Robert G. Wilson v *)

More terms from Stefan Steinerberger and Robert G. Wilson v, Jan 12 2006

Terms a(28) onward from Max Alekseyev, Dec 18 2011

cp's OEIS Frontend

A046063 Numbers k such that the k-th partition number A000041(k) is prime.

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A111036 Numbers n such that p(6n) is prime, where p(n) is the number of partitions of n.

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A111045 Numbers n such that P(4n) is prime, where P(m) is the number of partitions of m.

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A114165 Numbers n such that p(2n) is prime, where p(n) is the number of partitions of n.

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A114166 Numbers n such that p(5n) is prime, where p(n) is the number of partitions of n.

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A114167 Numbers n such that p(7n) is prime, where p(n) is the number of partitions of n.

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A114168 Numbers n such that p(8n) is prime, where p(n) is the number of partitions of n.

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A114169 Numbers n such that p(9n) is prime, where p(n) is the number of partitions of n.

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