A351713 - OEIS

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

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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