A351713 Numbers whose binary and minimal Lucas representations are both palindromic.
0, 9, 31, 975, 297097, 816867, 4148165871, 152488124529, 1632977901693, 11162529166917, 11925833175477, 3047549778123957, 3894487365191355, 8920885515768255
Offset: 1
Examples
n a(n) A007088(a(n)) A130310(a(n)) ---------------------------------------------------------- 1 0 0 0 2 9 1001 10001 3 31 11111 10000001 4 975 1111001111 100010000010001 5 297097 1001000100010001001 100001000000101000000100001
Crossrefs
Programs
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Mathematica
lucasPalQ[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; PalindromeQ[IntegerDigits[Total[2^s], 2]]]; Join[{0}, Select[Range[1, 10^6, 2], PalindromeQ[IntegerDigits[#, 2]] && lucasPalQ[#] &]]