A076992 Given a(1), ..., a(n-1), a(n) is minimal such that all terms of the sequence are distinct positive integers and, for all k>=1, the sum of the k terms from a(k) to a(2k-1) is a k-th power.

1, 2, 7, 3, 17, 4, 57, 5, 160, 6, 497, 8, 1454, 9, 4422, 10, 13117, 11, 39515, 12, 118092, 13, 354778, 14, 1062876, 15, 3190085, 16, 9565931, 18, 28702218, 19, 86093433, 20, 258293423, 21, 774840968, 22, 2324562427, 23, 6973568791, 24, 20920824474, 25

Offset

1,2

Comments

For even n, a(n) is just the smallest positive integer not already in the sequence. For odd n>=3, say n=2k-1, a(n) = 3^k - (a(k)+...+a(n-1)).

Links

Table of n, a(n) for n=1..44.

Mathematica

a[n_] := a[n]=Module[{s, sm, i, k}, s=Table[a[i], {i, 1, n-1}]; If[EvenQ[n], For[i=1, MemberQ[s, i], i++, Null]; Return[i]]; sm=Sum[a[i], {i, k=(n+1)/2, n-1}]; For[i=Ceiling[(sm+1)^(1/k)], MemberQ[s, i^k-sm], i++, Null]; i^k-sm]

Crossrefs

Sequence in context: A279357 A099130 A362359 * A138751 A112303 A336854

Adjacent sequences: A076989 A076990 A076991 * A076993 A076994 A076995

Keyword

nonn

Author

Amarnath Murthy, Oct 25 2002

Extensions

Edited by Dean Hickerson, Dec 02 2002

Status

approved