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

Author

Amiram Eldar, Feb 17 2022

Keywords

• nonn
• base

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.

Examples

			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
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to palindromes.

Crossrefs

Cf. A000032, A000211, A130310.

Subsequence of A054770.

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

Programs

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]