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 A113535 Ascending descending base exponent transform of the tribonacci substitution (A100619). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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][]; 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

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Last modified October 1 22:38 EDT 2023. Contains 365828 sequences. (Running on oeis4.)