A331191 - OEIS

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

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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.