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A134862 Wythoff ABB numbers. 11

%I #20 Aug 11 2022 03:21:21

%S 8,21,29,42,55,63,76,84,97,110,118,131,144,152,165,173,186,199,207,

%T 220,228,241,254,262,275,288,296,309,317,330,343,351,364,377,385,398,

%U 406,419,432,440,453,461,474,487,495,508,521,529,542,550,563,576,584,597

%N Wythoff ABB numbers.

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

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

%o (Python)

%o from math import isqrt

%o def A134862(n): return 5*(n+isqrt(5*n**2)>>1)+3*n # _Chai Wah Wu_, Aug 10 2022

%Y Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, 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

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)