A285087 Numbers n such that the number of partitions of n^2-1 is prime.

2, 13, 21, 46909

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, ", ")))
(Python)
from itertools import count, islice
from sympy import isprime, npartitions
def A285087_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: isprime(npartitions(n**2-1)), count(max(startvalue, 1)))
A285087_list = list(islice(A285087_gen(), 3)) # Chai Wah Wu, Nov 20 2023

Crossrefs

Cf. A000041, A046063, A072213, A284594, A285086, A285088.

Sequence in context: A333216 A303669 A084651 * A085509 A127485 A061385

Adjacent sequences: A285084 A285085 A285086 * A285088 A285089 A285090

Keyword

nonn,hard,more

Author

Serge Batalov, Apr 09 2017

Status

approved