A167968 - OEIS

%I #14 May 27 2024 11:31:48

%S 1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,

%T 2,1,3,2,1,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3,2,1,4,3,

%U 2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1

%N Signature sequence of phi^4 = 0.14589803375032..., where phi is the golden ratio minus 1 (0.61803398874989...).

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

%H <a href="/index/Si#signature_sequences">Index entries for sequences related to signature sequences</a>

%t terms = 105; m = Ceiling[Sqrt[terms]]; s0 = {}; While[s = (Table[i + j*(GoldenRatio-1)^4, {i, 1, m}, {j, 1, m}] // Flatten // SortBy[#, N]&)[[1 ;; terms]] /. GoldenRatio -> 1; s != s0, s0 = s; m = 2m]; s (* _Jean-François Alcover_, Jan 08 2017 *)

%Y Cf. A084531, A084532, A167972.

%K nonn

%O 1,8

%A _Casey Mongoven_, Nov 15 2009