A073698 a(n) is smallest prime not already in the sequence such that the sum of the first n terms is an n-th power.

2, 7, 503, 113, 7151, 109873, 162287, 2251875110689, 1423309560546093919, 1831931738588396657, 266306005917953213327, 13573982207668041076860262513, 4485809513902758532742979512207

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..100

Example

Sum of two terms 2+7 = 9 = 3^2. Sum of three terms 2+7+503 = 512 = 8^3.

Mathematica

a[n_] := a[n]=Module[{sm, i}, sm=Sum[a[i], {i, 1, n-1}]; For[k=Ceiling[(sm+2)^(1/n)], !ProvablePrimeQ[k^n-sm]||MemberQ[a/@Range[n-1], k^n-sm], k++, Null]; k^n-sm] (* First do <<NumberTheory`PrimeQ` *)

Crossrefs

Cf. A093927, A093928, A093929, A093355.

Sequence in context: A260229 A321134 A027732 * A073860 A093926 A065590

Adjacent sequences: A073695 A073696 A073697 * A073699 A073700 A073701

Keyword

nonn

Author

Amarnath Murthy, Aug 12 2002

Extensions

Edited by Dean Hickerson, Dec 02 2002

Status

approved