This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A133117 #4 Aug 19 2019 17:07:39
%S A133117 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,
%T A133117 3,8
%N A133117 Fractal sequence based on comparison of {n * tau} with {i*tau} for i = 1 to F(2j) where F(2j) equals the first i for which {n*tau} <= {i*tau} 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 {i*tau} 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.
%C A133117 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.
%F A133117 See A132827.
%e A133117 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}
%Y A133117 Cf. A054065, A132827, A132917, A132828.
%K A133117 nonn,uned
%O A133117 1,2
%A A133117 _Kenneth J Ramsey_, Sep 13 2007