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 A113534 Ascending descending base exponent transform of the flipped tribonacci substitution (A092782). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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][]; 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: A130049 A259256 A056703 * A103831 A217519 A106357 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

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Last modified October 20 15:15 EDT 2019. Contains 328267 sequences. (Running on oeis4.)