A351717 Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.

0, 2, 3, 5, 6, 10, 12, 14, 17, 20, 28, 30, 34, 36, 42, 46, 56, 61, 75, 77, 85, 92, 94, 101, 107, 115, 122, 128, 150, 166, 176, 198, 200, 211, 219, 233, 244, 246, 260, 271, 277, 288, 296, 310, 321, 345, 360, 396, 405, 441, 469, 484, 520, 522, 544, 562, 570, 588

Offset: 1

Author

Amiram Eldar, Feb 17 2022

Keywords

• nonn
• base

Comments

A001610(n) = Lucas(n+1) - 1 is a term for all n, since A001610(0) = 0 has the representation 0 and the representation of Lucas(n+1) - 1 is n 1's for n > 0.

Examples

			The first 10 terms are:
   n  a(n)  A130311(a(n))
   ----------------------
   1   0               0
   2   2               1
   3   3              11
   4   5             101
   5   6             111
   6  10            1111
   7  12           10101
   8  14           11011
   9  17           11111
  10  20          101101
		

Links

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

Crossrefs

Cf. A000032, A001610, A130311.

Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712.

Programs

Mathematica

lazy = Select[IntegerDigits[Range[6000], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse @ LucasL[Range[0, Length[#] - 1]]] & /@ lazy; s = FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]; Join[{0}, Position[s, _?PalindromeQ] // Flatten]