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A355956 Index k of partition function p such that p(k) is a member of a cousin prime pair. 0
3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Because asymptotically the size of the partition number function p(n) ~ O(exp(sqrt(n))), and the probability of primality of p(n) ~ O(1/sqrt(n)) and the combined probability of primality of p(n) and p(n)+-4 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(12) > 4*10^7.
LINKS
EXAMPLE
5 is in the sequence because A000041(5) = 7 and 7 + 4 = 11 are cousin primes.
13 is in the sequence because A000041(13) = 101 and 101 - 4 = 97 are cousin primes.
PROG
(PARI) for(n=1, 10000, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-4)||ispseudoprime(p+4)), print1(n, ", ")))
CROSSREFS
Sequence in context: A064519 A331398 A048968 * A185737 A092862 A112863
KEYWORD
nonn,hard,more
AUTHOR
Serge Batalov, Jul 21 2022
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)