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

Author

Serge Batalov, Apr 09 2017

Keywords

• nonn
• hard
• more

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.

Examples

			a(3) = 8 is in the sequence because A000041(8*9/2) = 17977 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, A285086, A285087.

Programs

PARI

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