Search: id:A113257
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%I A113257
%S A113257 1,5,266,266257,4429250586,2978988815561863,722638800922610642480852,
%T A113257 22529984108212742763058965679103268,
%U A113257 57286470055793196612331429228839529219232484069
%N A113257 Ascending descending base exponent transform of squares (A000290).
%C A113257 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?
%F A113257 a(n) = SUM[from i = 1 to n] (i^2)^((n-i+1)^2). a(n) = SUM[from i = 1 
               to n] (A000290(i))^(A000290(n-i+1)).
%e A113257 a(1) = 1 because (1^2)^(1^2) = 1^1 = 1.
%e A113257 a(2) = 5 because (1^2)^(4^1) + (4^1)^(1^4) = 1^4 + 4^1 = 5.
%e A113257 a(3) = 266 = 1^9 + 4^4 + 9^1.
%e A113257 a(4) = 266257 = 1^16 + 4^9 + 9^4 + 16^1.
%e A113257 a(5) = 4429250586 = 1^25 + 4^16 + 9^9 + 16^4 + 25^1.
%e A113257 a(6) = 2978988815561863 = 1^36 + 4^25 + 9^16 + 16^9 + 25^4 + 36^1.
%e A113257 a(7) = 722638800922610642480852 = 1^49 + 4^36 + 9^25 + 16^16 + 25^9 + 
               36^4 + 49^1.
%e A113257 a(8) = 22529984108212742763058965679103268 = 1^64 + 4^49 + 9^36 + 16^25 
               + 25^16 + 36^9 + 49^4 + 64^1.
%e A113257 a(9) = 57286470055793196612331429228839529219232484069 = 1^81 + 4^64 
               + 9^49 + 16^36 + 25^25 + 36^16 + 49^9 + 64^4 + 81^1.
%Y A113257 Cf. A000290, A005408, A113122, A113153, A113154.
%Y A113257 Sequence in context: A079681 A086656 A034602 this_sequence A140001 A153322 
               A066210
%Y A113257 Adjacent sequences: A113254 A113255 A113256 this_sequence A113258 A113259 
               A113260
%K A113257 easy,nonn
%O A113257 1,2
%A A113257 Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006

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