A113257 Ascending descending base exponent transform of squares (A000290).

1, 5, 266, 268722, 4682453347, 2978988815561863, 722638800922610642480852, 22529984108212742763058965679103268, 57286470055793196612331429228839529219232484069

Offset

1,2

Comments

A003101 is the ascending descending base exponent transform of natural numbers A000027. The ascending descending base exponent transform applied to the Fibonacci numbers is A113122; applied to the tribonacci numbers is A113153; applied to the Lucas numbers is A113154. The smallest prime in this sequence is a(2) = 5. What is the next prime? What is the first square value after 1?

Links

G. C. Greubel, Table of n, a(n) for n = 1..30

Formula

a(n) = Sum_{i=1..n} (i^2)^((n-i+1)^2).

a(n) = Sum_{i=1..n} (A000290(i))^(A000290(n-i+1)).

Example

a(1) = 1 because (1^2)^(1^2) = 1^1 = 1.
a(2) = 5 because (1^2)^(4^1) + (4^1)^(1^4) = 1^4 + 4^1 = 5.
a(3) = 266 = 1^9 + 4^4 + 9^1.
a(4) = 268722 = 1^16 + 4^9 + 9^4 + 16^1.
a(5) = 4682453347 = 1^25 + 4^16 + 9^9 + 16^4 + 25^1.
a(6) = 2978988815561863 = 1^36 + 4^25 + 9^16 + 16^9 + 25^4 + 36^1.
a(7) = 722638800922610642480852 = 1^49 + 4^36 + 9^25 + 16^16 + 25^9 + 36^4 + 49^1.
a(8) = 22529984108212742763058965679103268 = 1^64 + 4^49 + 9^36 + 16^25 + 25^16 + 36^9 + 49^4 + 64^1.
a(9) = 57286470055793196612331429228839529219232484069 = 1^81 + 4^64 + 9^49 + 16^36 + 25^25 + 36^16 + 49^9 + 64^4 + 81^1.

Mathematica

Table[Sum[(k^2)^((n - k + 1)^2), {k, 1, n}], {n, 1, 10}] (* G. C. Greubel, May 18 2017 *)

Prog

(PARI) for(n=1, 10, print1(sum(k=1, n, (k^2)^((n-k+1)^2) ), ", ")) \\ G. C. Greubel, May 18 2017

Crossrefs

Cf. A000290, A005408, A113122, A113153, A113154.

Sequence in context: A034602 A175180 A238799 * A180820 A140001 A329610

Adjacent sequences: A113254 A113255 A113256 * A113258 A113259 A113260

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 07 2006

Extensions

a(4) and a(5) corrected by Giovanni Resta, Jun 13 2016

Status

approved