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 A134860 Wythoff AAB numbers; also, Fib101 numbers: those n for which the Zeckendorf expansion A014417(n) ends with 1,0,1. 14
 4, 12, 17, 25, 33, 38, 46, 51, 59, 67, 72, 80, 88, 93, 101, 106, 114, 122, 127, 135, 140, 148, 156, 161, 169, 177, 182, 190, 195, 203, 211, 216, 224, 232, 237, 245, 250, 258, 266, 271, 279, 284, 292, 300, 305, 313, 321, 326, 334, 339, 347, 355, 360, 368, 373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The lower and upper Wythoff sequences, A and B, satisfy the complementary equations AAB=AA+AB and AAB=A+2B-1. LINKS Aviezri S. Fraenkel, Complementary iterated floor words and the Flora game, SIAM J. Discrete Math. 24 (2010), no. 2, 570-588. - N. J. A. Sloane, May 06 2011 Clark Kimberling, Complementary equations and Wythoff Sequences, Journal of Integer Sequences, 11 (2008) Article 08.3.3. FORMULA a(n) = A(A(B(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence. MATHEMATICA With[{r = Map[Fibonacci, Range[2, 14]]}, Position[#, {1, 0, 1}][[All, 1]] &@ Table[If[Length@ # < 3, {}, Take[#, -3]] &@ IntegerDigits@ Total@ Map[FromDigits@ PadRight[{1}, Flatten@ #] &@ Reverse@ Position[r, #] &, Abs@ Differences@ NestWhileList[Function[k, k - SelectFirst[Reverse@ r, # < k &]], n + 1, # > 1 &]], {n, 373}]] (* Michael De Vlieger, Jun 09 2017 *) PROG (Python) from sympy import fibonacci def a(n):     x=0     while n>0:         k=0         while fibonacci(k)<=n: k+=1         x+=10**(k - 3)         n-=fibonacci(k - 1)     return x def ok(n): return str(a(n))[-3:]=="101" print([n for n in range(4, 501) if ok(n)]) # Indranil Ghosh, Jun 08 2017 CROSSREFS Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134861, A134862, 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. Set-wise difference A003622 \ A095098. Cf. A095089 (fib101 primes). Sequence in context: A036047 A045042 A095099 * A301001 A047958 A300747 Adjacent sequences:  A134857 A134858 A134859 * A134861 A134862 A134863 KEYWORD nonn AUTHOR Antti Karttunen, Jun 01 2004 and Clark Kimberling, Nov 14 2007 EXTENSIONS This is the result of merging two sequences which were really the same. - N. J. A. Sloane, Jun 10 2017 STATUS approved

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Last modified April 15 00:13 EDT 2021. Contains 342971 sequences. (Running on oeis4.)