A049575 Prime partition numbers.

2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557, 74878248419470886233, 1394313503224447816939

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), 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.

Formula

a(n) = A000041(A046063(n)) = A000040(A051143(n)). - M. F. Hasler, Oct 19 2008

A010051(a(n))*A167392(a(n)) = 1. - Reinhard Zumkeller, Nov 03 2009

Mathematica

lst={}; Do[a=PartitionsP[n]; If[PrimeQ[a], AppendTo[lst, a]], {n, 2*6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
Select[PartitionsP[Range[1000]], PrimeQ] (* Harvey P. Dale, Mar 11 2013 *)

Prog

(PARI) for(n=0, 10^3, my(p=numbpart(n)); if(isprime(p), print1(p, ", "))); \\ Joerg Arndt, May 09 2013

Crossrefs

Intersection of A000040 and A000041.

Cf. A046063, A051143.

Cf. A038753, A065728. - Reinhard Zumkeller, Nov 03 2009

Sequence in context: A062352 A033938 A069598 * A070028 A084836 A062351

Adjacent sequences: A049572 A049573 A049574 * A049576 A049577 A049578

Keyword

nonn,nice

Author

G. L. Honaker, Jr.

Extensions

More terms from James A. Sellers and Christian G. Bower, Oct 15 1999.

Status

approved