A113173 - OEIS

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A113173

Ascending descending base exponent transform of semiprimes (A001358).

256, 5392, 315361, 11667713, 717360537, 83932270482, 27775696582531, 22260761742531649, 109563850113131234720, 2013390472722146301196, 1899501614194512059559835, 85600281199526209989968735 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	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. a(7) is itself semiprime. The smallest primes in this sequence are a(3) = 315361 and a(4) = 11667713. What is the next prime?`
	FORMULA	`a(n) = SUM[from i = 1 to n] (semiprime(i))^(semiprime(n-i+1)). a(n) = SUM[from i = 1 to n] (A001358(i))^(A001358(n-i+1)).`
	EXAMPLE	`a(1) = 256 because semiprime(1)^semiprime(1) = 4^4 = 256.` `a(2) = 5392 because prime(1)^prime(2) + prime(2)^prime(1) = 4^6 + 6^4 = 5392.` `a(3) = 315361 because 4^9 + 6^6 + 9^4 = 315361.` `a(4) = 11667713 = 4^10 + 6^9 + 9^6 + 10^4.` `a(5) = 717360537 = 4^14 + 6^10 + 9^9 + 10^6 + 14^4.` `a(6) = 83932270482 = 4^15 + 6^14 + 9^10 + 10^9 + 14^6 + 15^4.` `a(7) = 27775696582531 = 4^21 + 6^15 + 9^14 + 10^10 + 14^9 + 15^6 + 21^4.` `a(8) = 22260761742531649 = 4^22 + 6^21 + 9^15 + 10^14 + 14^10 + 15^9 + 21^6 + 22^4.` `a(9) = 109563850113131234720 = 4^25 + 6^22 + 9^21 + 10^15 + 14^14 + 15^10 + 21^9 + 22^6 + 25^4.`
	CROSSREFS	`Cf. A001358, A005408, A113122, A113153, A113154.` `Sequence in context: A200790 A206110 A196152 * A195595 A204567 A077072` `Adjacent sequences: A113170 A113171 A113172 * A113174 A113175 A113176`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 07 2006`

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Last modified February 16 10:07 EST 2012. Contains 205904 sequences.