A137355 Slowest-increasing sequence of noncomposite numbers such that the partial sums of the sequence are perfect powers.

1, 3, 5, 7, 11, 37, 61, 71, 11971, 16057, 40697, 46679, 61547, 66889, 177839, 192781, 355643, 407977, 1082099, 1096621, 1100467, 1102537, 3369329, 3402271, 4442993, 4462307, 5293999, 5304701, 7099793, 7104607, 7342633, 7413467, 9448897, 9657503

Offset: 1

Author

R. J. Mathar, Mar 07 2008

Keywords

• nonn

Comments

Also the first differences of A137354.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..70

Crossrefs

Cf. A001597, A174722, A176578.

Programs

Mathematica

fQ[n_] := GCD @@ Last /@ FactorInteger@n > 1; p = 3; sp = 2; lst = {2}; While[p < 10^9, If[ fQ[sp + p], AppendTo[lst, p]; Print@p; sp = sp + p]; p = NextPrime@p]; lst

Extensions

Edited and extended by Robert G. Wilson v, Apr 20 2010