A035359 Number of partitions-into-distinct-parts of n (A000009) is a prime.

3, 4, 5, 7, 22, 70, 100, 495, 1247, 2072, 320397, 3335367, 16168775, 37472505, 52940251, 78840125, 81191852

Offset

1,1

Comments

No other terms below 10^8. - Max Alekseyev, Jul 10 2015

Links

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Partition Function Q

Eric Weisstein's World of Mathematics, Partition Function Q-Congruences

Example

From Gus Wiseman, Jan 13 2020: (Start)
Strict partitions of a(1) = 3 through a(4) = 7:
  (3)    (4)    (5)    (7)
  (2,1)  (3,1)  (3,2)  (4,3)
                (4,1)  (5,2)
                       (6,1)
                       (4,2,1)
(End)

Mathematica

n = 1; A035359 = {}; While[n < 10^7, n++; If[ PrimeQ[ PartitionsQ[n]], Print[n]; AppendTo[A035359, n]]]; A035359 (* Jean-François Alcover, Oct 12 2011 *)

Crossrefs

The non-strict version is A046063.

The version for powers of 2 instead of primes is A331022.

The version for factorizations instead of strict partitions is A330991.

The version for strict factorizations instead of strict partitions is A331201.

Cf. A000009, A051005, A056848, A265835.

Sequence in context: A295988 A216433 A101761 * A365577 A325410 A269719

Adjacent sequences: A035356 A035357 A035358 * A035360 A035361 A035362

Keyword

nonn,nice,hard,more

Author

Olivier Gérard

Extensions

More terms from Eric W. Weisstein

a(12) from Max Alekseyev, Jul 04 2009

a(13)-a(14) from Giovanni Resta, Jun 05 2015, Jun 11 2015

a(15)-a(17) from Max Alekseyev, Jul 10 2015

Status

approved