A167970 - OEIS

%I #13 May 27 2024 11:32:17

%S 1,1,1,2,1,2,1,2,1,3,2,1,3,2,1,3,2,4,1,3,2,4,1,3,2,4,1,3,5,2,4,1,3,5,

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

%U 6,3,5,2,7,4,1,6,3,8,5,2,7,4,1,6,3,8,5,2,7,4,1,6,3,8,5,2,7,4,9,1,6,3,8,5,2

%N Signature sequence of phi^2 = 0.38196601125011..., where phi is the golden ratio 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^2, {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 *)

%Y Cf. A084531, A084532, A118276.

%K nonn

%O 1,4

%A _Casey Mongoven_, Nov 15 2009