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A113533 Ascending descending base exponent transform of the infinite Fibonacci word (A003842). 2
1, 3, 6, 5, 7, 12, 10, 15, 14, 14, 23, 16, 20, 27, 21, 30, 27, 25, 40, 28, 37, 38, 32, 49, 36, 40, 53, 39, 54, 49, 43, 68, 45, 55, 66, 50, 71, 60, 56, 83, 57, 74, 75, 61, 92, 67, 73, 94, 68, 93, 84, 72, 113, 75, 94, 101, 79, 116, 89, 91, 122, 86, 115, 108, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The infinite Fibonacci word b(n) is the fixed point of the morphism 1->12, 2->1, starting from b(1) = 2. This transform a(n) of that sequence b(n) satisfies n <= a(n) <= 4*n, but that is not a tight bound.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{k=1..n} A003842(k)^(A003842(n-k+1)). - G. C. Greubel, May 18 2017

EXAMPLE

a(1) = A003842(1)^A003842(1) = 1^1 = 1.

a(2) = A003842(1)^A003842(2) + A003842(2)^A003842(1) = 1^2 + 2^1 = 3.

a(3) = 1^1 + 2^2 + 1^1 = 6.

a(4) = 1^1 + 2^1 + 1^2 + 1^1 = 5.

a(5) = 1^2 + 2^1 + 1^1 + 1^2 + 2^1 = 7.

a(6) = 1^1 + 2^2 + 1^1 + 1^1 + 2^2 + 1^1 = 12.

a(7) = 1^2 + 2^1 + 1^2 + 1^1 + 2^1 + 1^2 + 2^1 = 10.

a(8) = 1^1 + 2^2 + 1^1 + 1^2 + 2^1 + 1^1 + 2^2 + 1^1 = 15.

a(9) = 1^1 + 2^1 + 1^2 + 1^1 + 2^2 + 1^1 + 2^1 + 1^2 + 1^1 = 14.

a(10) = 1^2 + 2^1 + 1^1 + 1^2 + 2^1 + 1^2 + 2^1 + 1^1 + 1^2 + 2^1 = 14.

MATHEMATICA

A003842[n_] := n + 1 - Floor[((1 + Sqrt[5])/2)*Floor[2*(n + 1)/(1 + Sqrt[5])]]; Table[Sum[A003842[k]^(A003842[n - k + 1]), {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, May 18 2017 *)

CROSSREFS

Cf. A003842, A005408, A087316, A113122, A113153, A113154, A113208, A113231, A113257, A113258, A113271, A113320, A113336, A113498.

Sequence in context: A247581 A175650 A272976 * A201418 A123688 A082284

Adjacent sequences:  A113530 A113531 A113532 * A113534 A113535 A113536

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jan 13 2006

EXTENSIONS

Corrected and extended by Giovanni Resta, Jun 13 2016

STATUS

approved

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Last modified February 20 04:35 EST 2018. Contains 299358 sequences. (Running on oeis4.)