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A285086 Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime. 8
1, 2, 3914 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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(4) > 90000.
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(2) = 2 is in the sequence because A000041(2^2+1) = 7 is a prime.
PROG
(PARI) for(n=1, 3920, if(ispseudoprime(numbpart(n^2+1)), print1(n, ", ")))
CROSSREFS
Sequence in context: A372116 A350418 A114573 * A367436 A024035 A048831
KEYWORD
nonn,hard,more,bref
AUTHOR
Serge Batalov, Apr 09 2017
STATUS
approved

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Last modified August 26 07:40 EDT 2024. Contains 375454 sequences. (Running on oeis4.)