A351718 Numbers whose binary and maximal Lucas representations are both palindromic.

0, 3, 5, 17, 85, 107, 219, 1161, 1365, 1619, 2047, 4097, 6141, 19801, 25027, 68961, 91213, 134337, 1540157, 1804859, 11877549, 37696497, 44092437, 142710801, 548269377, 3387848595, 4073444175, 8226780335, 31029923047, 64662095631, 67947722943, 126590440407, 2145176968607

Offset: 1

Author

Amiram Eldar, Feb 17 2022

Keywords

• nonn
• base

Examples

			The first 10 terms are:
   n   a(n)  A007088(a(n))    A130311(a(n))
   ----------------------------------------
   1     0               0                0
   2     3              11               11
   3     5             101              101
   4    17           10001            11111
   5    85         1010101        101101101
   6   107         1101011        111010111
   7   219        11011011      10110101101
   8  1161     10010001001   11011111111011
   9  1365     10101010101  101010101010101
  10  1619     11001010011  101111010111101
		

Links

• Index entries for sequences related to palindromes.

Crossrefs

Intersection of A006995 and A351717.

Cf. A007088, A130310, A351713.

Programs

Mathematica

lazy = Select[IntegerDigits[Range[10^6], 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}, Select[Position[s, _?PalindromeQ] // Flatten, PalindromeQ[IntegerDigits[#, 2]] &]]