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A134862 Wythoff ABB numbers. 11
8, 21, 29, 42, 55, 63, 76, 84, 97, 110, 118, 131, 144, 152, 165, 173, 186, 199, 207, 220, 228, 241, 254, 262, 275, 288, 296, 309, 317, 330, 343, 351, 364, 377, 385, 398, 406, 419, 432, 440, 453, 461, 474, 487, 495, 508, 521, 529, 542, 550, 563, 576, 584, 597 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..54.

Clark Kimberling, Complementary equations and Wythoff Sequences, Journal of Integer Sequences, 11 (2008) Article 08.3.3.

FORMULA

a(n)=A(B(B(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence.

PROG

(Python)

from sympy import floor

from mpmath import phi

def A(n): return floor(n*phi)

def B(n): return floor(n*phi**2)

def a(n): return A(B(B(n))) # Indranil Ghosh, Jun 10 2017

CROSSREFS

Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134863, A035338, A134864, A035513.

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.

Sequence in context: A053750 A271921 A003249 * A302253 A090206 A139590

Adjacent sequences:  A134859 A134860 A134861 * A134863 A134864 A134865

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 14 2007

STATUS

approved

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Last modified October 21 12:36 EDT 2018. Contains 316419 sequences. (Running on oeis4.)