A113535 Ascending descending base exponent transform of the tribonacci substitution (A100619).

1, 3, 8, 19, 32, 9, 11, 16, 26, 19, 29, 24, 47, 70, 28, 31, 58, 89, 35, 50, 65, 108, 65, 51, 52, 90, 101, 82, 101, 88, 122, 63, 81, 92, 153, 110, 89, 125, 110, 92, 101, 155, 90, 127, 196, 142, 87, 138, 207, 112, 112, 135, 217, 150, 124, 115, 204, 245, 139, 158, 189, 268, 121, 155, 154

Offset

1,2

Comments

Sirvent comments that in spite of the similarity of this map to the one in A092782, the two sequences have very different properties. They have different complexities, different Rauzy fractals, etc.

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

V. F. Sirvent, Semigroups and the self-similar structure of the flipped tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29. [Contains many further references.]

Formula

a(n) = Sum_{k=1..n} A100619(k)^(A100619(n-k-1)). - G. C. Greubel, May 18 2017

Example

a(1) = A100619(1)^A100619(1) = 1^1 = 1.
a(2) = A100619(1)^A100619(2) + A100619(2)^A100619(1) = 1^2 + 2^1 = 3.
a(3) = 1^3 + 2^2 + 3^1 = 8.
a(4) = 1^1 + 2^3 + 3^2 + 1^1 = 19.
a(5) = 1^1 + 2^1 + 3^3 + 1^2 + 1^1 = 32.
a(6) = 1^1 + 2^1 + 3^1 + 1^3 + 1^2 + 1^1 = 9.
a(7) = 1^2 + 2^1 + 3^1 + 1^1 + 1^3 + 1^2 + 2^1 = 11.
a(8) = 1^1 + 2^2 + 3^1 + 1^1 + 1^1 + 1^3 + 2^2 + 1^1 = 16.
a(9) = 1^1 + 2^1 + 3^2 + 1^1 + 1^1 + 1^1 + 2^3 + 1^2 + 2^1 = 26.
a(10) = 1^1 + 2^2 + 3^1 + 1^2 + 1^1 + 1^1 + 2^1 + 1^3 + 2^2 + 1^1 = 19.
a(11) = 1^2 + 2^1 + 3^2 + 1^1 + 1^2 + 1^1 + 2^1 + 1^1 + 2^3 + 1^2 + 2^1 = 29.
a(12) = 1^3 + 2^2 + 3^1 + 1^2 + 1^1 + 1^2 + 2^1 + 1^1 + 2^1+ 1^3 + 2^2 + 3^1 = 24.

Mathematica

A100619:= Nest[Function[l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {3, 1}, 3 -> {1}})]}], {1}, 8][[1]]; Table[Sum[(A100619[[k]])^(A100619[[n-k+1]]), {k, 1, n}], {n, 1, 100}] (* G. C. Greubel, May 18 2017 *)

Crossrefs

Cf. A100619, A092782, A103269, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208, A113498.

Sequence in context: A219391 A123982 A171308 * A184444 A139020 A147358

Adjacent sequences: A113532 A113533 A113534 * A113536 A113537 A113538

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 13 2006

Extensions

Terms a(13) to a(50) from G. C. Greubel, May 18 2017

Terms a(51) onward added by G. C. Greubel, Jan 03 2019

Status

approved