A285088 Numbers n such that the number of partitions of n(n+1)/2 (=A000041(A000217(n))) is prime.

2, 3, 8, 3947, 43968, 61681

Offset

1,1

Comments

Because asymptotically A000041(n*(n+1)/2) ~ exp(Pi*sqrt(2/3*(n*(n+1)/2))) / (4*sqrt(3)*(n*(n+1)/2)), the sum of the prime probabilities ~1/log(A000041(n*(n+1)/2)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.

Links

Table of n, a(n) for n=1..6.

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(3) = 8 is in the sequence because A000041(8*9/2) = 17977 is a prime.

Prog

(PARI) for(n=1, 2000, if(ispseudoprime(numbpart(n*(n+1)/2)), print1(n, ", ")))

Crossrefs

Cf. A000041, A046063, A072213, A284594, A285086, A285087.

Sequence in context: A132502 A113840 A336292 * A075849 A005604 A114020

Adjacent sequences: A285085 A285086 A285087 * A285089 A285090 A285091

Keyword

nonn,hard,more

Author

Serge Batalov, Apr 09 2017

Status

approved