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 A113271 Ascending descending base exponent transform of 2^n. 9
 1, 3, 9, 41, 593, 135457, 8606778433, 36893769626691833985, 680564733921105089459460297630318346497, 231584178474632390853419071752762496470716041121409734167406717963826481922561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 primes in this (always odd) sequence are a(1) = 3, a(3) = 41 and a(5) = 543. What is the next prime? LINKS G. C. Greubel, Table of n, a(n) for n = 0..12 FORMULA a(n) = Sum_{i=0..n} (2^i)^(2^(n-i)). a(n) = Sum_{i=0..n} (2^(n-i))^(2^i). a(n) = Sum_{i=0..n} (A000079(i))^(A000079(n-i)). EXAMPLE a(0) = 1 because (2^0)^(2^0) = 1^1 = 1. a(1) = 3 = (2^0)^(2^1) + (2^1)^(2^0) = 1^2 + 2^1. a(2) = 9 = (2^0)^(2^2) + (2^1)^(2^1) + (2^2)^(2^0) = 1^4 + 2^2 + 4^1. a(3) = 41 = 1^8 + 2^4 + 4^2 + 8^1. a(4) = 593 = 1^16 + 2^8 + 4^4 + 8^2 + 16^1 a(5) = 135457 = 1^32 + 2^16 + 4^8 + 8^4 + 16^2 + 32^1. a(6) = 8606778433 = 1^64 + 2^32 + 4^16 + 8^8 + 16^4 + 32^2 + 64^1. a(7) = 36893769626691833985 = 1^128 + 2^64 + 4^32 + 8^16 + 16^8 + 32^4 + 64^2 + 128^1. a(8) = 680564733921105089459460297630318346497 = 1^256 + 2^128 + 4^64 + 8^32 + 16^16 + 32^8 + 64^4 + 128^2 + 256^1. MATHEMATICA Table[Sum[(2^k)^(2^(n - k)), {k, 0, n}], {n, 0, 10}] (* G. C. Greubel, May 19 2017 *) PROG (PARI) for(n=0, 5, print1(sum(k=0, n, (2^k)^(2^(n-k))), ", ")) \\ G. C. Greubel, May 19 2017 CROSSREFS Cf. A000079, A005408, A113122, A113153, A113154. Sequence in context: A109743 A139150 A293955 * A249045 A183306 A057724 Adjacent sequences:  A113268 A113269 A113270 * A113272 A113273 A113274 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 07 2006 EXTENSIONS a(4) corrected by Giovanni Resta, Jun 13 2016 Formulas corrected by G. C. Greubel, May 19 2017 STATUS approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)