A331191 Numbers whose dual Zeckendorf representations (A104326) are palindromic.

0, 1, 3, 4, 6, 11, 12, 16, 19, 22, 32, 33, 38, 42, 48, 53, 64, 71, 87, 88, 98, 106, 110, 118, 124, 134, 142, 148, 174, 194, 205, 231, 232, 245, 255, 271, 284, 288, 304, 317, 323, 336, 346, 362, 375, 402, 420, 462, 474, 516, 548, 566, 608, 609, 635, 656, 666, 687

Offset

1,3

Comments

Pairs of numbers of the form {F(2*k-1)-2, F(2*k-1)-1}, for k >= 2, where F(k) is the k-th Fibonacci number, are consecutive terms in this sequence: {0, 1}, {3, 4}, {11, 12}, {32, 33}, ... - Amiram Eldar, Sep 03 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4 is a term since its dual Zeckendorf representation, 101, is palindromic.

Mathematica

mirror[dig_, s_] := Join[dig, s, Reverse[dig]];
select[v_, mid_] := Select[v, Length[#] == 0 || Last[#] != mid &];
fib[dig_] := Plus @@ (dig * Fibonacci[Range[2, Length[dig] + 1]]);
pals = Join[{{}}, Rest[Select[IntegerDigits[Range[0, 2^6 - 1], 2], SequenceCount[#, {0, 0}] == 0 &]]];
Union@Join[{0}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 0]), mirror[#, {0}] & /@ (select[pals, 0]), mirror[#, {1}] & /@ pals]]

Crossrefs

Cf. A000045, A002113, A006995, A014190, A094202, A104326.

Sequence in context: A352734 A275418 A047413 * A294917 A115018 A057030

Adjacent sequences: A331188 A331189 A331190 * A331192 A331193 A331194

Keyword

nonn,base

Author

Amiram Eldar, Jan 11 2020

Status

approved