A285086 - OEIS

A285086

Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime.

1, 2, 3914

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OFFSET

1,2

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(4) > 90000.

LINKS

Table of n, a(n) for n=1..3.

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

EXAMPLE

a(2) = 2 is in the sequence because A000041(2^2+1) = 7 is a prime.

PROG

(PARI) for(n=1, 3920, if(ispseudoprime(numbpart(n^2+1)), print1(n, ", ")))

CROSSREFS

Cf. A000041, A046063, A072213, A284594, A285087, A285088.