A355956 Index k of partition function p such that p(k) is a member of a cousin prime pair.

3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060

Offset: 1

Author

Serge Batalov, Jul 21 2022

Keywords

• nonn
• hard
• more

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.

Examples

			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.
		

Crossrefs

Cf. A000041, A046063, A072213, A285086, A285087, A285088, A284594, A355704-A355706.

Programs

PARI

for(n=1, 10000, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-4)||ispseudoprime(p+4)), print1(n, ", ")))