A167969 Signature sequence of phi^3 = 0.23606797749979..., where phi is the golden ratio 0.61803398874989... .

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 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, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 7, 3, 4, 5, 1, 6, 2, 7, 3, 4, 5, 1, 6

Offset

1,6

References

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

Links

Table of n, a(n) for n=1..105.

Mathematica

terms = 105; m = Ceiling[Sqrt[terms]]; s0 = {}; While[s = (Table[i + j/GoldenRatio^3, {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 *)

Crossrefs

Cf. A084531, A084532, A167971.

Sequence in context: A161262 A161287 A214069 * A245192 A235431 A354599

Adjacent sequences: A167966 A167967 A167968 * A167970 A167971 A167972

Keyword

nonn

Author

Casey Mongoven, Nov 15 2009

Status

approved