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

1,2

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

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 *)

Crossrefs

Cf. A084531, A084532, A167970.

Sequence in context: A125159 A179548 A023119 * A023123 A023131 A356625

Adjacent sequences: A118273 A118274 A118275 * A118277 A118278 A118279

Keyword

nonn

Author

Casey Mongoven, Apr 21 2006

Status

approved