A113257 - OEIS

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A113257

Ascending descending base exponent transform of squares (A000290).

1, 5, 266, 266257, 4429250586, 2978988815561863, 722638800922610642480852, 22529984108212742763058965679103268, 57286470055793196612331429228839529219232484069 (list; graph; refs; listen; history; 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?`
	FORMULA	`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)).`
	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) = 266257 = 1^16 + 4^9 + 9^4 + 16^1.` `a(5) = 4429250586 = 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.`
	CROSSREFS	`Cf. A000290, A005408, A113122, A113153, A113154.` `Sequence in context: A086656 A034602 A175180 * A180820 A140001 A153322` `Adjacent sequences: A113254 A113255 A113256 * A113258 A113259 A113260`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006`

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Last modified February 13 12:17 EST 2012. Contains 205469 sequences.