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Number of partitions-into-distinct-parts of n (A000009) is a prime.
23

%I #42 Jan 13 2020 13:54:25

%S 3,4,5,7,22,70,100,495,1247,2072,320397,3335367,16168775,37472505,

%T 52940251,78840125,81191852

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

%C No other terms below 10^8. - _Max Alekseyev_, Jul 10 2015

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionQ.html">Partition Function Q</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionQCongruences.html">Partition Function Q-Congruences</a>

%e From _Gus Wiseman_, Jan 13 2020: (Start)

%e Strict partitions of a(1) = 3 through a(4) = 7:

%e (3) (4) (5) (7)

%e (2,1) (3,1) (3,2) (4,3)

%e (4,1) (5,2)

%e (6,1)

%e (4,2,1)

%e (End)

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

%Y The non-strict version is A046063.

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

%Y The version for factorizations instead of strict partitions is A330991.

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

%Y Cf. A000009, A051005, A056848, A265835.

%K nonn,nice,hard,more

%O 1,1

%A _Olivier Gérard_

%E More terms from _Eric W. Weisstein_

%E a(12) from _Max Alekseyev_, Jul 04 2009

%E a(13)-a(14) from _Giovanni Resta_, Jun 05 2015, Jun 11 2015

%E a(15)-a(17) from _Max Alekseyev_, Jul 10 2015