A120929 Partial sums of n^(n^2), A002489.

1, 2, 18, 19701, 4294986997, 298023228171940122, 10314424798788558774343889178, 256923577521069192513410265783009965210785, 6277101735386681020759366944276858929512621227473999723681

Offset

0,2

Comments

After 2, can this ever be prime? This is to A001923 Sum k^k, k=1..n, as k^k^k is to k^k.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..26

Formula

a(n) = Sum_{i=0..n} i^(i^2). a(n) = Sum_{i=0..n} (i^i)^i. In this sequence, we formally define 0^0 = 1.

Example

a(0) = 1 because A002489(0) is given formally as 0^0^0 = 1.
a(1) = 2 because 1 + (1^1)^1 = 1 + 1 = 2.
a(2) = 18 because 2 + (2^2)^2 = 2 + 16 = 18.
a(3) = 19701 because 18 + (3^3)^3 = 18 + 19683 = 19701.
a(4) = 4294986997 = 19701 + (4^4)^4 = 19701 + 4294967296.

Mathematica

Accumulate[Join[{1}, Table[n^(n^2), {n, 9}]]] (* Harvey P. Dale, Apr 10 2014 *)

Crossrefs

Cf. A001923, A002489, A002488, A001329, A002488, A023813, A076113, A090588.

Sequence in context: A276092 A191554 A066361 * A349886 A007184 A067765

Adjacent sequences: A120926 A120927 A120928 * A120930 A120931 A120932

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 18 2006

Extensions

More terms from Harvey P. Dale, Apr 10 2014

Status

approved