OFFSET
1,1
COMMENTS
Because asymptotically the size of the partition number function p(n) is ~ O(exp(sqrt(n))), and the probability of primality of p(n) is ~ O(1/sqrt(n)) and the combined probability of primality of p(n) and p(n+1) is ~ O(1/n), the sum of the prime probabilities is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.
a(6) > 10^8.
PROG
(PARI) for(k=1, 5000, if(ispseudoprime(numbpart(k))&&ispseudoprime(numbpart(k+1)), print1(k, ", ")))
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Serge Batalov, Jul 15 2022
STATUS
approved