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

1,1

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

Links

Table of n, a(n) for n=1..35.

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A034784 A190280 A261786 * A292526 A151747 A088597

Adjacent sequences: A124398 A124399 A124400 * A124402 A124403 A124404

Keyword

nonn,more

Author

Artur Jasinski, Dec 14 2006

Extensions

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

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

Status

approved