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A098020 Let f[n] = fractional part of n*Pi and let g[x] = -1 for the range 0<=x<=1/3, g[x] = 0 for the range 1/3<x<=2/3, g[x] = 11 for range 2/3<x<1. Sequence gives all positive integers n such that f[n+2]-2*f[n+1]+f[n]-g[f[n+1]] = 0. 0

%I #10 Jan 02 2024 14:12:21

%S 2,3,9,10,16,17,23,24,30,31,37,38,39,44,45,46,51,52,53,58,59,60,65,66,

%T 67,72,73,74,80,81,87,88,94,95,101,102,108,109,115,116,122,123,129,

%U 130,136,137,143,144,150,151,152,157,158,159,164,165,166,171,172,173,178

%N Let f[n] = fractional part of n*Pi and let g[x] = -1 for the range 0<=x<=1/3, g[x] = 0 for the range 1/3<x<=2/3, g[x] = 11 for range 2/3<x<1. Sequence gives all positive integers n such that f[n+2]-2*f[n+1]+f[n]-g[f[n+1]] = 0.

%C Irrational rotation of Pi as an implicit sequence with an uneven Cantor cartoon.

%t f[n_]=Mod[Pi*n, 1]; digits=200; (* uneven Cantor type function*); g[x_]:=-1/ ;0<=x<=1/3; g[x_]:=0/;1/3<x<=2/3; g[x_]:=11/;1/3<x<=1; a=Delete[Union[Table[If [N[f[n+2]-2*f[n+1]+f[n]]-g[f[n+1]]==0, n, 0], {n, 1, digits}]], 1]

%K nonn

%O 1,1

%A _Roger L. Bagula_, Sep 09 2004

%E Edited by _N. J. A. Sloane_, Jun 24 2007

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)