A118276 - OEIS

%I #20 May 27 2024 11:17:27

%S 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,

%T 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,

%U 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

%N Signature sequence of Phi^2 = 2.618033989... (A104457), where Phi is the golden ratio A001622.

%C Equals A023119 in the first 98 terms, then the sequences differ. [From _R. J. Mathar_, Aug 08 2008]

%D C. Kimberling, "Fractal Sequences and Interspersions", Ars Combinatoria, vol. 45 p 157 1997.

%H T. D. Noe, <a href="/A118276/b118276.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SignatureSequence.html">Signature Sequence</a>

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

%t 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 *)

%Y Cf. A084531, A084532, A167970.

%K nonn

%O 1,2

%A _Casey Mongoven_, Apr 21 2006