A341333 - OEIS

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A341333

Positions of palindromes in the ordering of all 01-words defined at A341258.

1, 2, 3, 6, 7, 9, 11, 13, 19, 20, 23, 25, 29, 32, 39, 43, 53, 54, 60, 65, 67, 72, 76, 82, 87, 91, 107, 119, 126, 142, 143, 151, 157, 167, 175, 177, 187, 195, 199, 207, 213, 223, 231, 248, 259, 285, 292, 318, 338, 349, 375, 376, 392, 405, 411, 424, 434, 450

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Among the first 20 words (0,1,00,01,10,000,11,001,010,100,000,011,101,0001,110,0010,0100,1000,00000,111), there are 10 palindromes: 0,1,00,000,11,010,000,101,00000,111; these begin at positions 1,2,3,6,7,9,11,13,19, respectively.

MATHEMATICA

z = 800; r = (1 + Sqrt[5])/2;

s = Table[Floor[r*n], {n, 1, z}]; (* A000201 *)

t = Complement[Range[Max[s]], s]; (* A001950 *)

s1[n_] := Length[Intersection[Range[n - 1], s]];

t1[n_] := n - 1 - s1[n];

w[1] = {0}; w[t[[1]]] = {1};

w[n_] := If[MemberQ[s, n], Join[{0}, w[s1[n]]], Join[{1}, w[t1[n]]]]

tt = Table[w[n], {n, 1, z}]; Select[tt, # == Reverse[#] &];

Select[Range[Length[tt]], tt[[#]] == Reverse[tt[[#]]] &] (* A341333 *)

CROSSREFS

Cf. A341258.