A285086 Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime.

1, 2, 3914

Offset: 1

Author

Serge Batalov, Apr 09 2017

Keywords

• nonn
• hard
• more
• bref

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.

Examples

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

Links

• 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

Crossrefs

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

Programs

PARI

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