A130311 -id:A130311 - cp's OEIS frontend

A195121 a(n) = 2*n - floor(n/r), where r = (1 + sqrt(5))/2 (the golden ratio).

0, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 88, 89, 90, 92, 93, 94

Offset: 0

Clark Kimberling, Sep 09 2011

nonn

Apparently, the nonzero terms are the numbers whose maximal Lucas representation (A130311) ends with 1. - Amiram Eldar, Jan 21 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Cf. A001622, A130311.

[3*n-Floor(n*(1+Sqrt(5))/2): n in [0..70]]; // Vincenzo Librandi, Sep 12 2011

Table[2n-Floor[n/GoldenRatio],{n,0,70}] (* Harvey P. Dale, Feb 11 2018 *)

a(n) = 3*n - floor(n*r), where r = (1 + sqrt(5))/2.

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

Original entry on oeis.org

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

Amiram Eldar, Feb 17 2022

			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

Index entries for sequences related to palindromes.

Intersection of A006995 and A351717.

Cf. A007088, A130310, A351713.

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]] &]]

cp's OEIS Frontend

A195121 a(n) = 2*n - floor(n/r), where r = (1 + sqrt(5))/2 (the golden ratio).

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