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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 December 10 00:30 EST 2018. Contains 318032 sequences. (Running on oeis4.)