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A113271
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Ascending descending base exponent transform of 2^n.
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9
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1, 3, 9, 41, 593, 135457, 8606778433, 36893769626691833985, 680564733921105089459460297630318346497, 231584178474632390853419071752762496470716041121409734167406717963826481922561
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OFFSET
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0,2
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COMMENTS
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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?
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n} (2^i)^(2^(n-i)).
a(n) = Sum_{i=0..n} (2^(n-i))^(2^i).
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EXAMPLE
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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.
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MATHEMATICA
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Table[Sum[(2^k)^(2^(n - k)), {k, 0, n}], {n, 0, 10}] (* G. C. Greubel, May 19 2017 *)
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PROG
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(PARI) for(n=0, 5, print1(sum(k=0, n, (2^k)^(2^(n-k))), ", ")) \\ G. C. Greubel, May 19 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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