OFFSET
1,3
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..29
EXAMPLE
3 is a term since both its binary and dual Zeckendorf representations are 11 which is palindromic.
33 is a term since its binary representation, 100001, and its dual Zeckendorf representation, 1010101, are both 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 /@ FromDigits /@ Tuples[{0, 1}, 22], SequenceCount[#, {0, 0}] == 0 &]]];
dualZeckPals = Union @ Join[{0}, fib /@ Join[mirror[#, {}] & /@ (select[pals, 0]), mirror[#, {0}] & /@ (select[pals, 0]), mirror[#, {1}] & /@ pals]];
binPalQ[n_] := PalindromeQ@IntegerDigits[n, 2]; Select[dualZeckPals, binPalQ]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 11 2020
EXTENSIONS
a(18)-a(22) from Chai Wah Wu, Jan 12 2020
a(23)-a(25) from Chai Wah Wu, Jan 13 2020
STATUS
approved