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Numbers k such that A061015(k) is prime.
1

%I #10 Jun 28 2022 15:27:36

%S 2,10,18,36,90,759

%N Numbers k such that A061015(k) is prime.

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

%C a(7) > 1850. - _Michael S. Branicky_, Jun 27 2022

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

%e 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.

%o (PARI) sm(n)= s=0;for(i=1,n,s=s+1/(prime(i)^2));return(s);

%o for (i=1,400,if(isprime(numerator(sm(i))),print1(i,",")))

%o (Python) # uses A061015gen() and imports from A061015

%o from sympy import isprime

%o def agen():

%o yield from (k for k, ak in enumerate(A061015gen(), 1) if isprime(ak))

%o print(list(islice(agen(), 5))) # _Michael S. Branicky_, Jun 27 2022

%Y Cf. A061015.

%K hard,nonn

%O 1,1

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

%E a(6) from _Alexander Adamchuk_, Sep 16 2010