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

1, 2, 3914

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.

Sequence in context: A372116 A350418 A114573 * A367436 A024035 A048831

Adjacent sequences: A285083 A285084 A285085 * A285087 A285088 A285089

Keyword

nonn,hard,more,bref

Author

Serge Batalov, Apr 09 2017

Status

approved