1,3

a(9) has 429 digits. 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. There is no nontrivial integer fixed point of the transform.

a(1) = 1. For n>1: a(n) = (1/2) * SUM[from i = 1 to n] (a(i))^a(n-i+1).

a(2) = 1 because a(1)^a(2) + a(2)^a(1) = 1^1 + 1^1 = 2 and 2/2 = 1.

a(3) = 2 because a(1)^a(3) + a(2)^a(2) + a(3)^a(1) = 1^2 + 1^1 + 2^1 = 4 and 4/2 = 2.

a(4) = 4 because a(1)^a(4) + a(2)^a(3) + a(3)^a(2) + a(4)^a(1) = 1^4 + 1^2 + 2^1 + 4^1 = 8 and 8/2 = 4.

a(5) = 10 because a(1)^a(5) + a(2)^a(4) + a(3)^a(3) + a(4)^a(2) + a(5)^a(1) = 1^10 + 1^4 + 2^2 + 4^1 + 10^1 = 20 and 20/2 = 10.

a(6) = 44 because 1^44 + 1^10 + 2^4 + 4^2 + 10^1 + 44^1 = 88 and 88/2 = 44.

a(7) = (1^1426 + 1^44 + 2^10 + 4^4 + 10^2 + 44^1 + 1426^1)/2 = 1426.

a(8) = (1^17592187106356 + 1^1426 + 2^44 + 4^10 + 10^4 + 44^2 + 1426^1 + 17592187106356^1)/2 = 17592187106356.

Cf. A113122, A113153, A113154.

Sequence in context: A013549 A125805 A028404 this_sequence A000613 A053500 A080090

Adjacent sequences: A113205 A113206 A113207 this_sequence A113209 A113210 A113211

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 06 2006