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Search: id:A113534
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| A113534 |
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Ascending descending base exponent transform of the flipped tribonacci substitution (A092782). |
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+0
2
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| 1, 3, 4, 7, 20, 10, 39, 12, 26, 19, 20, 43
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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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.]
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EXAMPLE
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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 = 4.
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.
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CROSSREFS
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Cf. A092782, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208, A113498.
Adjacent sequences: A113531 A113532 A113533 this_sequence A113535 A113536 A113537
Sequence in context: A041497 A042227 A117789 this_sequence A030724 A124082 A056655
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 13 2006
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