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

1,2

Links

Table of n, a(n) for n=1..14.

Index entries for sequences related to palindromes.

Example

   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

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[#] &]]

Crossrefs

Intersection of A006995 and A351712.

Subsequence of A054770.

Cf. A007088, A130310.

Similar sequences: A095309, A331193, A331894, A351718.

Sequence in context: A266710 A159279 A048547 * A141573 A075433 A018833

Adjacent sequences: A351710 A351711 A351712 * A351714 A351715 A351716

Keyword

nonn,base,more

Author

Amiram Eldar, Feb 17 2022

Status

approved