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A124401 Indices where 2 occurs in A124151. 4

%I

%S 3,5,8,9,11,15,21,39,50,63,83,95,99,173,350,854,1308,1769,2903,5250,

%T 5345,5639,6195,7239,21368,41669,47684,58619,63515,69468,70539,133508,

%U 134993,187160,493095

%N Indices where 2 occurs in A124151.

%C Does 2 occur infinitely often in A124151?

%C 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)-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

%F A127936 \ A006093. - _R. J. Mathar_, Feb 03 2010

%t 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 *)

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 14 2006

%E More terms from _Robert G. Wilson v_, Dec 17 2006

%E a(24)-a(35) from _R. J. Mathar_, Feb 03 2010

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Last modified July 15 14:07 EDT 2019. Contains 325030 sequences. (Running on oeis4.)