A092062 Numbers k such that A061015(k) is prime.

2, 10, 18, 36, 90, 759

Offset: 1

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004

Keywords

• hard
• nonn

Comments

a(6) > 447 for a(6) the numerator has more than 2673 digits.

a(7) > 1850. - Michael S. Branicky, Jun 27 2022

Examples

			1/2^2 = 1/4 but 1 is not prime, 1/2^2 + 1/3^2 = 13/36 and 13 is prime so a(1)=2.
		

Crossrefs

Cf. A061015.

Programs

PARI

sm(n)= s=0;for(i=1,n,s=s+1/(prime(i)^2));return(s);
for (i=1,400,if(isprime(numerator(sm(i))),print1(i,",")))

Python

# uses A061015gen() and imports from A061015
from sympy import isprime
def agen():
    yield from (k for k, ak in enumerate(A061015gen(), 1) if isprime(ak))
print(list(islice(agen(), 5))) # Michael S. Branicky, Jun 27 2022

Formula

Numbers k such that numerator of (Sum_{i=1..k} 1/prime(i)^2) is prime

Extensions

a(6) from Alexander Adamchuk, Sep 16 2010