cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A074292 Dominant digit in successive groups of 3 from the Kolakoski sequence (A000002).

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%I A074292 #47 Oct 02 2018 20:05:11
%S A074292 2,1,2,2,1,1,2,1,2,1,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,
%T A074292 1,2,2,1,1,2,1,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,2,2,1,1,2,1,2,1,1,2,1,2,
%U A074292 2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1
%N A074292 Dominant digit in successive groups of 3 from the Kolakoski sequence (A000002).
%C A074292 This appears to be the same as a sequence studied by Claude Lenormand in a letter dated Nov 17 2003: break up the Kolakoski sequence (A000002) into runs of identical symbols and omit one symbol from each run.
%C A074292 The sequence studied by Claude Lenormand is A156257 and is not equal to this one: see A248805 = A156257 - A074292. Differences between the two sequences are at n = 47, 48, 56, 57, 128, 129, 137, 139, 147, 148, 176, 177,... - _Jean-Christophe Hervé_, Oct 11 2014
%C A074292 As in the Kolakoski sequence, runs in this sequence are of length 1 or 2, because a run XX implies the repetition of exactly the same 3-group in the Kolakoski sequence: -YXX-YXX- or -XXY-XXY- or -XYX-XYX-, and this is not possible 3 times. However, words of the form YXYXY appear in this sequence, but don't appear in the Kolakoski sequence. - _Jean-Christophe Hervé_, Oct 12 2014
%H A074292 Nathaniel Johnston, <a href="/A074292/b074292.txt">Table of n, a(n) for n = 1..10001</a>
%H A074292 Claude Lenormand, <a href="/A318921/a318921.pdf">Deux transformations sur les mots</a>, Preprint, 5 pages, Nov 17 2003. Apparently unpublished. This is a scanned copy of the version that the author sent to me in 2003. - _N. J. A. Sloane_, Oct 02 2018
%F A074292 a(n)=A000002(3n-2)+A000002(3n-1)+A000002(3n)-3. - _Benoit Cloitre_, Nov 15 2003
%e A074292 Kolakoski begins (1,2,2), (1,1,2), (1,2,2), (1,2,2), so this begins 2,1,2,2.
%p A074292 A074292 := proc(n)
%p A074292     A000002(3*n-2)+A000002(3*n-1)+A000002(3*n)-3 ;
%p A074292 end proc:
%p A074292 seq(A074292(n),n=1..50) ; # _R. J. Mathar_, Nov 15 2014
%t A074292 OK = {1, 2, 2}; Do[OK = Join[OK, {1+Mod[n-1, 2]}], {n, 3, 1000}, {OK[[n]]}]; If[Count[#, 1] > 1, 1, 2]& /@ Partition[OK, 3]  (* _Jean-François Alcover_, Nov 13 2014 *)
%Y A074292 Cf. A000002, A074293, A074295, A156257, A248805, A318921.
%K A074292 nonn
%O A074292 1,1
%A A074292 _Jon Perry_, Sep 21 2002
%E A074292 More terms from _Ray Chandler_, Nov 16 2003
%E A074292 Offset corrected by _Jean-Christophe Hervé_, Oct 11 2014