cp's OEIS Frontend

A184516 Lower s-Wythoff sequence, where s=4n-2. Complement of A184517.

%I A184516 #13 Jan 05 2025 19:51:39
%S A184516 1,2,4,5,6,7,9,10,11,12,13,15,16,17,18,20,21,22,23,25,26,27,28,30,31,
%T A184516 32,33,34,36,37,38,39,41,42,43,44,46,47,48,49,51,52,53,54,56,57,58,59,
%U A184516 60,62,63,64,65,67,68,69,70,72,73,74,75,77,78,79,80,81,83,84,85,86,88,89,90,91,93,94,95,96,98,99,100,101,102,104,105,106,107,109,110,111,112,114,115,116,117,119,120,121,122,123,125,126,127,128,130,131,132,133,135,136,137,138,140,141,142,143,145,146,147,148
%N A184516 Lower s-Wythoff sequence, where s=4n-2.  Complement of A184517.
%C A184516 See A184117 for the definition of lower and upper s-Wythoff sequences.
%H A184516 G. C. Greubel, <a href="/A184516/b184516.txt">Table of n, a(n) for n = 1..10000</a>
%H A184516 Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/49-3/KimberlingGeneralized.pdf">Beatty Sequences and Wythoff Sequences, Generalized</a>, Fibonacci Quart. 49 (2011), no. 3, 195-200.
%t A184516 k = 4; r = 2; d = Sqrt[4 + k^2];
%t A184516 a[n_] := Floor[(1/2) (d + 2 - k) (n + r/(d + 2))];
%t A184516 b[n_] := Floor[(1/2) (d + 2 + k) (n - r/(d + 2))];
%t A184516 Table[a[n], {n, 120}] (* A184516 *)
%t A184516 Table[b[n], {n, 120}] (* A184517 *)
%o A184516 (PARI) vector(100, n, floor((sqrt(5)-1)*(n + 1/(1+sqrt(5))))) \\ _G. C. Greubel_, Nov 16 2018
%o A184516 (Magma) [Floor((Sqrt(5)-1)*(n + 1/(1+Sqrt(5)))): n in [1..100]]; // _G. C. Greubel_, Nov 16 2018
%o A184516 (Sage) [floor((sqrt(5)-1)*(n + 1/(1+sqrt(5)))) for n in (1..100)] # _G. C. Greubel_, Nov 16 2018
%Y A184516 Cf. A184117, A184517.
%K A184516 nonn
%O A184516 1,2
%A A184516 _Clark Kimberling_, Jan 16 2011