A038601 Prime numbers p such that the number of partitions of p is also a prime.
2, 3, 5, 13, 157, 491, 863, 1621, 2633, 5347, 8117, 13513, 35227, 62311, 76367, 84017, 141637, 170537, 189353, 192667, 201821, 216617, 251677, 269257, 288203, 293621, 353807, 366103, 367621, 372023, 441703, 444167, 478571, 518657, 582371, 626333, 780707, 816521
Offset: 1
Keywords
Examples
5 = (1+1+1+1+1+1,1+1+1+2,1+1+3,1+4,1+2+2,2+3,5), so partition(5) = 7; 5 and 7 are primes.
Links
- Hisanori Mishima, Partition Number (n = 0 to 1000): Factorizations.
- Hisanori Mishima, Partition Number (n = 1001 to 2000): Factorizations.
- Hisanori Mishima, Partition Number (n = 2001 to 3000); Factorizations.
- Hisanori Mishima, Partition Number (n = 3001 to 4000): Factorizations.
- Hisanori Mishima, Partition Number (n = 4001 to 5000): Factorizations.
- Hisanori Mishima, Partition Number (n = 5001 to 6000): Factorizations.
- Hisanori Mishima, Partition Number (n = 6001 to 7000): Factorizations.
- Hisanori Mishima, Partition Number (n = 7001 to 8000): Factorizations.
- Hisanori Mishima, Partition Number (n = 8001 to 9000): Factorizations.
- Hisanori Mishima, Partition Number (n = 9001 to 10000): Factorizations.
- Hisanori Mishima, Factorization of Partition Number.
Programs
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Mathematica
Do[ If[ PrimeQ[n] && PrimeQ[ PartitionsP[n]], Print[n]], {n, 1, 10^5} ]
Extensions
More terms from Simon Plouffe
More terms from Robert G. Wilson v, Aug 29 2001
a(17)-a(36) from Jacques Tramu, Jun 26 2005
Corrected by T. D. Noe, Oct 31 2006
Offset changed and a(37)-a(38) from Michael S. Branicky, Jun 24 2025