A285087 - OEIS

A285087

Numbers n such that the number of partitions of n^2-1 is prime.

2, 13, 21, 46909

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OFFSET

1,1

COMMENTS

Because asymptotically A000041(n^2-1) ~ exp(Pi*sqrt(2/3*(n^2-1))) / (4*sqrt(3)*(n^2-1)), the sum of the prime probabilities ~1/log(A000041(n^2-1)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.

a(5) > 50000.

LINKS

Table of n, a(n) for n=1..4.

Chris K. Caldwell, Top twenty prime partition numbers, The Prime Pages.

Eric Weisstein's World of Mathematics, Partition Function P

Eric Weisstein's World of Mathematics, Integer Sequence Primes

FORMULA

{n: A000041(n^2-1) in A000040}.

EXAMPLE

13 is in the sequence because A000041(13^2-1) = 228204732751 is a prime.

PROG

(PARI) for(n=1, 2000, if(ispseudoprime(numbpart(n^2-1)), print1(n, ", ")))