A167967 Signature sequence of phi^5 = 0.090169943749474..., where phi is the inverse golden ratio A094214.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3

Offset: 1

Author

Casey Mongoven, Nov 15 2009

Keywords

• nonn

References

• Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.

Links

• Index entries for sequences related to signature sequences

Crossrefs

Cf. A084531, A084532, A167973.

Programs

Mathematica

terms = 105; m = Ceiling[Sqrt[terms]]; s0 = {}; While[s = (Table[i + j/GoldenRatio^5, {i, 1, m}, {j, 1, m}] // Flatten // SortBy[#, N] &)[[1 ;; terms]] /. GoldenRatio -> \[Infinity]; s != s0, s0 = s; m = 2 m]; s (* Jean-François Alcover, Jan 08 2017 *)