A124401 Indices where 2 occurs in A124151.

3, 5, 8, 9, 11, 15, 21, 39, 50, 63, 83, 95, 99, 173, 350, 854, 1308, 1769, 2903, 5250, 5345, 5639, 6195, 7239, 21368, 41669, 47684, 58619, 63515, 69468, 70539, 133508, 134993, 187160, 493095

Offset: 1

Author

Artur Jasinski, Dec 14 2006

Keywords

• nonn
• more

Comments

Does 2 occur infinitely often in A124151?

The sum in A124151 is 1+n if k=1, and 1+k*(k^(2n)-1)/(k^2-1) if k>1. The indices of A124151(n)=2 are where k=1 is avoided, but where k=2 leads to a prime, i.e., where 1+n is not prime but 1+2*(4^n-1)/3 = (2^(2n+1)+1)/3 is prime. Therefore this sequence here is constructed by taking all n=(A000978(i)-1)/2 (the members of A127936), and eliminating cases with 1+n in A000040. - R. J. Mathar, Feb 03 2010

Crossrefs

Cf. A006093, A124151, A124154, A124163, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124205-A124209.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[ Sum[k^(2j - 1), {j, n}] + 1] && k < 3, k++ ]; k]; lst = {}; Do[ If[f@n == 2, Print[n]; AppendTo[lst, n]], {n, 9250}]; lst (* Robert G. Wilson v, Dec 17 2006 *)

PARI

is(n) = !isprime(n+1) && isprime(1 + 2*(4^n-1)/3); \\ Amiram Eldar, Oct 24 2024

Formula

A127936 \ A006093. - R. J. Mathar, Feb 03 2010

Extensions

More terms from Robert G. Wilson v, Dec 17 2006

a(24)-a(35) from R. J. Mathar, Feb 03 2010