A176578 -id:A176578 - cp's OEIS frontend

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

R. J. Mathar, Mar 07 2008

nonn

Also the first differences of A137354.

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

Cf. A001597, A174722, A176578.

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

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

A174722 Slowest increasing sequence of odd primes such that the partial sums of the sequence from the second on are perfect powers.

Original entry on oeis.org

3, 5, 17, 103, 233, 1367, 1753, 2351, 7393, 19543, 20593, 46639, 54449, 284527, 344249, 407791, 512009, 812431, 844433, 1214407, 1316033, 2109671, 2233601, 11251351, 11267777, 13903271, 14449489, 16203287, 16451713, 18219679, 18367721, 18529111

Offset: 1

Giovanni Teofilatto, Mar 28 2010

nonn

			3+5=8, 3+5+17=25, 3+5+17+103=128 are perfect powers, i.e., in A007504.

Robert G. Wilson v, Table of n, a(n) for n = 1..71

Cf. A001597, A137355, A176578.

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

Edited and extended by R. J. Mathar, Mar 31 2010

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions