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%I #33 Mar 27 2024 08:48:05
%S 7,20,28,41,54,62,75,83,96,109,117,130,143,151,164,172,185,198,206,
%T 219,227,240,253,261,274,287,295,308,316,329,342,350,363,376,384,397,
%U 405,418,431,439,452,460,473,486,494,507,520,528,541,549,562,575,583,596
%N Wythoff BAB numbers.
%C The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BAB=2A+3B-1.
%C Also numbers with suffix string 1010, when written in Zeckendorf representation. - _A.H.M. Smeets_, Mar 24 2024
%H A.H.M. Smeets, <a href="/A134863/b134863.txt">Table of n, a(n) for n = 1..20000</a>
%H Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, Journal of Integer Sequences 11 (2008) Article 08.3.3.
%F a(n) = B(A(B(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence.
%F From _A.H.M. Smeets_, Mar 24 2024: (Start)
%F a(n) = 2*A(n) + 3*B(n) - 1 (see Clark Kimberling 2008), with A=A000201, B=A001950, the lower and upper Wythoff sequences, respectively.
%F Equals {A035336}\{A134861} (= Wythoff BA \ Wythoff BAA). (End)
%o (Python)
%o from sympy import floor
%o from mpmath import phi
%o def A(n): return floor(n*phi)
%o def B(n): return floor(n*phi**2)
%o def a(n): return B(A(B(n))) # _Indranil Ghosh_, Jun 10 2017
%o (Python)
%o from math import isqrt
%o def A134863(n): return 5*(n+isqrt(5*n**2)>>1)+3*n-1 # _Chai Wah Wu_, Aug 11 2022
%Y Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134862, A035338, A134864, A035513.
%Y 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.
%K nonn
%O 1,1
%A _Clark Kimberling_, Nov 14 2007
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