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A035338 4th column of Wythoff array.

%I A035338 #44 Mar 28 2025 11:43:12
%S A035338 5,18,26,39,52,60,73,81,94,107,115,128,141,149,162,170,183,196,204,
%T A035338 217,225,238,251,259,272,285,293,306,314,327,340,348,361,374,382,395,
%U A035338 403,416,429,437,450,458,471,484,492,505,518,526,539,547,560,573,581,594
%N A035338 4th column of Wythoff array.
%C A035338 The asymptotic density of this sequence is 1/phi^5 = phi^5 - 11 = A244593 - 4 = 0.0901699... . - _Amiram Eldar_, Mar 24 2025
%H A035338 Seiichi Manyama, <a href="/A035338/b035338.txt">Table of n, a(n) for n = 0..10000</a>
%H A035338 Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, <a href="https://arxiv.org/abs/2503.19696">Fibonacci-like partitions and their associated piecewise-defined permutations</a>, arXiv:2503.19696 [math.CO], 2025. See p. 5.
%H A035338 John H. Conway and N. J. A. Sloane, <a href="/A019586/a019586.pdf">Notes on the Para-Fibonacci and related sequences</a>.
%H A035338 Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, JIS, Vol. 11 (2008), Article 08.3.3.
%H A035338 N. J. A. Sloane, <a href="/classic.html#WYTH">Classic Sequences</a>.
%p A035338 t := (1+sqrt(5))/2 ; [ seq(5*floor((n+1)*t)+3*n,n=0..80) ];
%t A035338 f[n_] := 5 Floor[(n + 1) GoldenRatio] + 3n; Array[f, 54, 0] (* _Robert G. Wilson v_, Dec 11 2017 *)
%o A035338 (Python)
%o A035338 from math import isqrt
%o A035338 def A035338(n): return 5*(n+1+isqrt(5*(n+1)**2)>>1)+3*n # _Chai Wah Wu_, Aug 11 2022
%Y A035338 Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864. The eight triples AAA, AAB, ..., BBB are A134859, A134860, A035337, A134862, A134861, A134863, A035338, A134864, resp.
%Y A035338 Cf. A035513, A244593.
%K A035338 nonn
%O A035338 0,1
%A A035338 _N. J. A. Sloane_ and _J. H. Conway_