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A285088
Numbers n such that the number of partitions of n(n+1)/2 (=A000041(A000217(n))) is prime.
8
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
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
KEYWORD
nonn,hard,more
AUTHOR
Serge Batalov, Apr 09 2017
STATUS
approved