A118276 Signature sequence of Phi^2 = 2.618033989... (A104457), where Phi is the golden ratio A001622.

1, 2, 3, 1, 4, 2, 5, 3, 6, 1, 4, 7, 2, 5, 8, 3, 6, 1, 9, 4, 7, 2, 10, 5, 8, 3, 11, 6, 1, 9, 4, 12, 7, 2, 10, 5, 13, 8, 3, 11, 6, 14, 1, 9, 4, 12, 7, 15, 2, 10, 5, 13, 8, 16, 3, 11, 6, 14, 1, 9, 17, 4, 12, 7, 15, 2, 10, 18, 5, 13, 8, 16, 3, 11, 19, 6, 14, 1, 9, 17, 4, 12, 20, 7, 15, 2, 10, 18, 5, 13

Offset: 1

Author

Casey Mongoven, Apr 21 2006

Keywords

• nonn

Comments

Equals A023119 in the first 98 terms, then the sequences differ. [From R. J. Mathar, Aug 08 2008]

References

• C. Kimberling, "Fractal Sequences and Interspersions", Ars Combinatoria, vol. 45 p 157 1997.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Signature Sequence
• Index entries for sequences related to signature sequences

Crossrefs

Cf. A084531, A084532, A167970.

Programs

Mathematica

terms = 90; m = Ceiling[Sqrt[terms]]; s0 = {}; While[s = (Table[i + j*GoldenRatio^2, {i, 1, m}, {j, 1, m}] // Flatten // SortBy[#, N] &)[[1 ;; terms]] /. GoldenRatio -> 0; s != s0, s0 = s; m = 2 m]; s (* Jean-François Alcover, Jan 08 2017 *)