A351712 Numbers whose minimal (or greedy) Lucas representation (A130310) is palindromic.

0, 2, 6, 9, 13, 20, 24, 31, 49, 56, 64, 78, 100, 125, 136, 150, 158, 169, 201, 237, 252, 324, 342, 364, 378, 396, 404, 422, 444, 523, 581, 606, 650, 708, 845, 874, 910, 932, 961, 975, 1004, 1040, 1048, 1077, 1113, 1135, 1164, 1366, 1460, 1500, 1572, 1666, 1692, 1786

Offset

1,2

Comments

A000211(n) = Lucas(n) + 2 is a term for all n > 2, since the representation of Lucas(n) + 2 is 10...01 with n-1 0's between the two 1's.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to palindromes.

Example

The first 10 terms are:
   n  a(n) A130310(a(n))
   ---------------------
   1   0               0
   2   2               1
   3   6            1001
   4   9           10001
   5  13          100001
   6  20         1000001
   7  24         1001001
   8  31        10000001
   9  49       100000001
  10  56       100010001

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]]]; Select[Range[0, 2000], lucasPalQ]

Crossrefs

Cf. A000032, A000211, A130310.

Subsequence of A054770.

Similar sequences: A002113, A006995, A014190, A094202, A331191, A351717.

Sequence in context: A076522 A372061 A094111 * A181021 A048162 A226823

Adjacent sequences: A351709 A351710 A351711 * A351713 A351714 A351715

Keyword

nonn,base

Author

Amiram Eldar, Feb 17 2022

Status

approved