A113534 Ascending descending base exponent transform of the flipped tribonacci substitution (A092782).

1, 3, 6, 7, 20, 10, 39, 12, 26, 19, 20, 43, 21, 78, 24, 53, 30, 57, 43, 88, 61, 59, 56, 43, 90, 42, 155, 46, 109, 53, 122, 75, 105, 114, 73, 122, 62, 197, 63, 172, 71, 136, 96, 183, 140, 122, 139, 86, 179, 81, 304, 83, 185, 98, 153, 162, 160, 261, 121, 192, 107, 236, 126

Offset

1,2

Comments

The flipped tribonacci substitution (A092782) b(n) is the fixed point of the morphism 1 -> 12, 2 -> 13, 3 -> 1, starting from b(1) = 1. The transformed sequence a(n) satisfies n <= a(n) <= 27 n but the bound can be determined to be much tighter.

Links

Table of n, a(n) for n=1..63.

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} A092782(k)^(A092782(n-k+1)). - G. C. Greubel, May 17 2017

Example

a(1) = A092782(1)^A092782(1) = 1^1 = 1.
a(2) = A092782(1)^A092782(2) + A092782(2)^A092782(1) = 1^2 + 2^1 = 3.
a(3) = 1^1 + 2^2 + 1^1 = 6.
a(4) = 1^3 + 2^1 + 1^2 + 3^1 = 7.
a(5) = 1^1 + 2^3 + 1^1 + 3^2 + 1^1 = 20.
a(6) = 1^2 + 2^1 + 1^3 + 3^1 + 1^2 + 2^1 = 10.
a(7) = 1^1 + 2^2 + 1^1 + 3^3 + 1^1 + 2^2 + 1^1 = 39.
a(8) = 1^1 + 2^1 + 1^2 + 3^1 + 1^3 + 2^1 + 1^2 + 1^1 = 12.
a(9) = 1^2 + 2^1 + 1^1 + 3^2 + 1^1 + 2^3 + 1^1 + 1^2 + 2^1 = 26.
a(10) = 1^1 + 2^2 + 1^1 + 3^1 + 1^2 + 2^1 + 1^3 + 1^1 + 2^2 + 1^1 = 19.
a(11) = 1^3 + 2^1 + 1^2 + 3^1 + 1^1 + 2^2 + 1^1 + 1^3 + 2^1 + 1^2 + 3^1 = 20.
a(12) = 1^1 + 2^3 + 1^1 + 3^2 + 1^1 + 2^1 + 1^2 + 1^1 + 2^3 + 1^1 + 3^2 + 1^1 = 43.

Mathematica

A092782[n_] := Nest[Function[l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}})]}], {1}, n][[1]]; Table[Sum[(A092782[k][[k]])^((A092782[n - k + 1][[n - k + 1]])), {k, 1, n}], {n, 1, 10}] (* G. C. Greubel, May 18 2017 *)

Crossrefs

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

Sequence in context: A341183 A259256 A056703 * A103831 A217519 A364007

Adjacent sequences: A113531 A113532 A113533 * A113535 A113536 A113537

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 13 2006

Extensions

a(3) corrected by Giovanni Resta, Jun 13 2016

a(13) onward from G. C. Greubel, May 18 2017

Status

approved