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

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

Author

Giovanni Teofilatto, Mar 28 2010

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A001597, A137355, A176578.

Programs

Mathematica

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

Extensions

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

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