A132917 -id:A132917 - cp's OEIS frontend

A132828 Sequence created based upon the value of the infinite Fibonacci word after truncating the first few terms built from placing 1,2,3.. into the sequence wherein each number is inserted at points based upon the value of the truncated Fibonacci word.

255, 253, 251, 250, 252, 248, 246, 245, 247, 243, 242, 244, 249, 240, 238, 237, 239, 235, 233, 232, 234, 230, 229, 231, 236, 227, 225, 224, 226, 222, 221, 223, 228, 241, 219, 217, 216, 218, 214, 212, 211, 213, 209, 208, 210, 215, 206, 204, 203, 205, 201

Offset: 0

Kenneth J Ramsey, Sep 03 2007

Related to A132827. See further comments there.

I am not certain this sequence is accurate, but it is still interesting. See comments in A132827.

			1, 3, 8, 21, 55, 144, ... appear at the end of the sequence presumably since the infinite word after truncating the first 0, 2, 7, 20, 54, 143 terms has more 1's to the left side of the sequence. Consider the value where the terms to the right are 2 raised to increasingly negative powers.

Kenneth J Ramsey, Sep 03 2007, Table of n, a(n) for n = 0..254

Cf. A132827, A132917, A133117.

A133117 Fractal sequence based on comparison of {n * tau} with {itau} for i = 1 to F(2j) where F(2j) equals the first i for which {ntau} <= {itau} as i goes from 1 to F(2j+2)-1 and F(2j) equals the insertion point of n into P(n-1). The fractional parts {itau} are all less than or equal to {F(2j-2)*tau} for 0 < i < F(2j), so there is no chance that an insertion point greater than n in the permutation of the first n-1 integers will be specified by this rule. The table, A132827, gives the insertion points for each n into the permutation P(n-1) of the first n integers.

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 3, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 8

Offset: 1

Kenneth J Ramsey, Sep 13 2007

This sequence is a modification of that in A054065 which gives the fractal series of the same permutation as the permutation of A132917 for which a couple of generating algorithms are given.

			The first few permutations are 1, 21, 213, 4213, 54213, 546213 since {6*tau} is greater than {1*Tau} but less than {3*Tau}; and since of 0<i<7 only {3*tau} and {6*tau} are greater than {1*tau}

Cf. A054065, A132827, A132917, A132828.

See A132827.

cp's OEIS Frontend

A132828 Sequence created based upon the value of the infinite Fibonacci word after truncating the first few terms built from placing 1,2,3.. into the sequence wherein each number is inserted at points based upon the value of the truncated Fibonacci word.

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