%I #35 Apr 02 2024 14:34:40

%S 2,10,15,23,31,36,44,49,57,65,70,78,86,91,99,104,112,120,125,133,138,

%T 146,154,159,167,175,180,188,193,201,209,214,222,230,235,243,248,256,

%U 264,269,277,282,290,298,303,311,319,324,332,337,345,353,358,366,371

%N Wythoff BAA numbers.

%C The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BAA=A+2B-3.

%C Also numbers with suffix string 0010, when written in Zeckendorf representation (with leading zero's for the first term). - _A.H.M. Smeets_, Mar 20 2024

%H A.H.M. Smeets, <a href="/A134861/b134861.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(A(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence.

%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(A(n))) # _Indranil Ghosh_, Jun 10 2017

%o (Python)

%o from math import isqrt

%o def A134861(n): return 3*((n+isqrt(5*n**2)>>1)-1)+(n<<1) # _Chai Wah Wu_, Aug 10 2022

%Y Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134862, A134863, 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