A341257 Positions of palindromes in the ordering of all 01-words defined at A341256.

1, 2, 3, 6, 7, 9, 12, 14, 15, 21, 24, 30, 31, 35, 41, 45, 48, 52, 58, 62, 63, 75, 81, 93, 96, 108, 114, 126, 127, 135, 147, 155, 161, 169, 181, 189, 192, 200, 212, 220, 226, 234, 246, 254, 255, 279, 291, 315, 321, 345, 357, 381, 384, 408, 420, 444, 450, 474

Offset

1,2

Comments

Also, the positions in A076478 of palindromes. - Clark Kimberling, Aug 16 2021

Links

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

Example

Among the first 20 words (0, 1, 00, 10, 01, 11, 000, 100, 010, 110, 001, 101, 011, 111, 0000, 1000, 0100, 1100, 0010, 1010), there are 9 palindromes: 0, 1, 00, 11, 000, 010, 101, 111, 0000, beginning in positions 1, 2, 3, 6, 7, 9, 12, 14, 15, respectively.

Mathematica

z = 800; s = Table[2 n - 1, {n, 1, z}];
t = Complement[Range[Max[s]], s];
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[#] &]
p = Select[Range[Length[tt]], tt[[#]] == Reverse[tt[[#]]] &]

Crossrefs

Cf. A341256.

Appears to equal A044051 - 2. - Hugo Pfoertner, Mar 16 2021

Sequence in context: A061951 A377994 A346301 * A153348 A246647 A177729

Adjacent sequences: A341254 A341255 A341256 * A341258 A341259 A341260

Keyword

nonn

Author

Clark Kimberling, Mar 16 2021

Status

approved