The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006345 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006345

Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix.
(history; published version)

#125 by Charles R Greathouse IV at Sun Feb 16 08:32:30 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/LinusSequence.html">Linus Sequence.</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#124 by Alois P. Heinz at Wed Jul 17 08:47:24 EDT 2024

STATUS

reviewed

approved

#123 by Stefano Spezia at Wed Jul 17 08:44:27 EDT 2024

STATUS

proposed

reviewed

#122 by Stefano Spezia at Wed Jul 17 08:44:24 EDT 2024

STATUS

editing

proposed

#121 by Stefano Spezia at Wed Jul 17 08:44:20 EDT 2024

LINKS

T. D. Noe, Robert Israel , and Hugo van der Sanden, <a href="/A006345/b006345.txt">Table of n, a(n) for n = 1..50000</a> (1..1000 from T. D. Noe, 1001..20000 from Robert Israel)

P. Balister, S. Kalikow, and A. Sarkar, <a href="http://www2.ims.nus.edu.sg/preprints/2007-19.pdf">The Linus sequence</a>, Preprint May 2007; Combinatorics, Probability and Computing, Volume 19, Issue 1 January 2010 , pp. 21-46..

N. Hellerstein, M. Gardner, & and S. Kim, <a href="/A006345/a006345_1.pdf">Correspondence related to the Linus and Sally sequences, 1977</a>

STATUS

reviewed

editing

#120 by Stefano Spezia at Wed Jul 17 08:43:51 EDT 2024

STATUS

proposed

reviewed

#119 by Jean-François Alcover at Wed Jul 17 08:13:51 EDT 2024

STATUS

editing

proposed

#118 by Jean-François Alcover at Wed Jul 17 08:12:48 EDT 2024

MATHEMATICA

a[1]=1; a[2]=2; suffix[lst_] := If[MatchQ[lst, {___, b__, b__}], lst /. {___, b__, b__} :> {b}, {}]; a[n_] := a[n] = Module[{aa, lg1, lg2}, aa = Array[a, n-1]; lg1 = suffix[Append[aa, 1]] // Length; lg2 = suffix[Append[aa, 2]] // Length; If[lg1 <= lg2, 1, 2]]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Dec 11 2014 *)

LDS[L_] := Module[{Cands, r, m}, Cands = Range[Floor[Length[L]/2]]; r = 0; For[m = 1, Length[Cands] > 0, m++, Cands = Select[Cands, L[[-m]] == L[[-# - m]]&]; If[Min[Cands] == m, r = m; Cands = ReplaceAll[Cands, m -> Nothing]]]; r]; A = {1}; For[n = 2, n <= 10^3, n++, If[LDS[Append[A, 1]] < LDS[Append[A, 2]], A = Append[A, 1], A = Append[A, 2]]];

Table[A[[i]], {i, 1, 105}] (* Jean-François Alcover, Jul 17 2024, after Robert Israel *)

STATUS

approved

editing

Discussion

Wed Jul 17

08:13

Jean-François Alcover: Previous Mma code was way too slow.

#117 by Michael De Vlieger at Wed Jul 10 20:32:05 EDT 2024

STATUS

proposed

approved

#116 by Robert C. Lyons at Wed Jul 10 19:46:10 EDT 2024

STATUS

editing

proposed