login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #24 Jan 21 2023 04:56:38

%S 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,

%T 35,36,38,39,41,42,43,45,46,47,49,50,52,53,54,56,57,59,60,61,63,64,65,

%U 67,68,70,71,72,74,75,77,78,79,81,82,83,85,86,88,89,90,92,93,94

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

%C Apparently, the nonzero terms are the numbers whose maximal Lucas representation (A130311) ends with 1. - _Amiram Eldar_, Jan 21 2023

%H Vincenzo Librandi, <a href="/A195121/b195121.txt">Table of n, a(n) for n = 0..10000</a>

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

%t Table[2n-Floor[n/GoldenRatio],{n,0,70}] (* _Harvey P. Dale_, Feb 11 2018 *)

%o (Magma) [3*n-Floor(n*(1+Sqrt(5))/2): n in [0..70]]; // _Vincenzo Librandi_, Sep 12 2011

%Y Cf. A001622, A130311.

%K nonn

%O 0,2

%A _Clark Kimberling_, Sep 09 2011