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 A317208 The Wythoff representation of n: an alternative way of presenting A189921. 10
 0, 1, 2, 12, 112, 22, 1112, 212, 122, 11112, 2112, 1212, 1122, 222, 111112, 21112, 12112, 11212, 2212, 11122, 2122, 1222, 1111112, 211112, 121112, 112112, 22112, 111212, 21212, 12212, 111122, 21122, 12122, 11222, 2222, 11111112, 2111112, 1211112, 1121112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is an encoding of the position of n in the A000201, A001950 "Wythoff" table T. Let T denote the following 3-rowed table, whose rows are n, A = A000201(n), B = A001950(n): n: 1 2 3 .4 .5 .6 .7 .8 .9 ... A: 1 3 4 .6 .8 .9 11 12 14 ... B: 2 5 7 10 13 15 18 20 23 ... Set a(0)=0. For n>0, locate n in rows A and B of the table, and indicate how to reach that entry starting from column 1. For example, 18 = B(7) = B(B(3)) = B(B(A(2))) = B(B(A(B(1)))), so the path to reach 18 is BBAB, which we write (encoding A as 1, B as 2) as a(18) = 2212. This is another way of writing the Wythoff representation of n described in Lang (1996) and A189921. REFERENCES W. Lang, The Wythoff and the Zeckendorf representations of numbers are equivalent, in G. E. Bergum et al. (edts.) Application of Fibonacci numbers vol. 6, Kluwer, Dordrecht, 1996, pp. 319-337. LINKS Lars Blomberg, Table of n, a(n) for n = 0..10000 W. Lang, The Wythoff and the Zeckendorf representations of numbers are equivalent, in G. E. Bergum et al. (edts.) Application of Fibonacci numbers vol. 6, Kluwer, Dordrecht, 1996, pp. 319-337. [Corrected scanned copy, with permission of the author.] CROSSREFS Cf. A189921, A135817 (length). Cf. also A317207. Sequence in context: A264916 A296644 A235860 * A207778 A102659 A212659 Adjacent sequences:  A317205 A317206 A317207 * A317209 A317210 A317211 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Aug 09 2018 EXTENSIONS a(23) and beyond from Lars Blomberg, Aug 11 2018 STATUS approved

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)