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A285087 Numbers n such that the number of partitions of n^2-1 is prime. 3
2, 13, 21, 46909 (list; graph; refs; listen; history; text; internal format)
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, ", ")))

CROSSREFS

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

Sequence in context: A182459 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

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)