A355704 - OEIS

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A355704

Indices k of partition function p where p(k) and p(k) + 2 are twin primes.

3, 4, 6, 13, 2335166

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OFFSET

1,1

COMMENTS

Because asymptotically size of partitions number function p(n) ~ O(exp(sqrt(n))), and probability of primality of p(n) ~ O(1/sqrt(n)) and combined probability of primality of p(n) and p(n)+-2 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) > 10^7.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

13 is a term because A000041(13) = 101 is prime and 103 is prime.

PROG

(PARI) for(n=1, 2500, if(ispseudoprime(p=numbpart(n))&&ispseudoprime(p+2), print1(n, ", ")))

CROSSREFS

Cf. A000041, A046063, A072213, A285086, A285087, A285088, A284594, A355705, A355706.

Sequence in context: A143100 A369545 A327584 * A180859 A271618 A137820

Adjacent sequences: A355701 A355702 A355703 * A355705 A355706 A355707

KEYWORD

nonn,hard,more

AUTHOR

Serge Batalov, Jul 14 2022

STATUS

approved