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

1,2

Links

Table of n, a(n) for n=1..33.

Index entries for sequences related to palindromes.

Example

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

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]] &]]

Crossrefs

Intersection of A006995 and A351717.

Cf. A007088, A130310, A351713.

Sequence in context: A102295 A365518 A227335 * A281627 A102846 A100003

Adjacent sequences: A351715 A351716 A351717 * A351719 A351720 A351721

Keyword

nonn,base

Author

Amiram Eldar, Feb 17 2022

Status

approved