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 A113257 Ascending descending base exponent transform of squares (A000290). 9
 1, 5, 266, 268722, 4682453347, 2978988815561863, 722638800922610642480852, 22529984108212742763058965679103268, 57286470055793196612331429228839529219232484069 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 23 08:51 EDT 2021. Contains 345395 sequences. (Running on oeis4.)