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

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.

Sequence in context: A344954 A181732 A338901 * A190199 A014873 A029467

Adjacent sequences: A341330 A341331 A341332 * A341334 A341335 A341336

Keyword

nonn

Author

Clark Kimberling, Mar 16 2021

Status

approved