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A156257
Digit of runs of length 2 in the Kolakoski sequence A000002: a(n) = A000002(A078649(n)).
4
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, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2
OFFSET
1,1
COMMENTS
Often equal to A074292 (at the beginning), but not always (see comments in A074292). First differences between the two sequences are at n = 47, 48, 56, 57, 128, 129, 137, 139, 147, 148,176, 177,... (see A248345 = A156257 - A074292). - Jean-Christophe Hervé, Oct 11 2014
As in the Kolakoski sequence, runs in this sequence are of length 1 or 2: a run XX in this sequence implies YXXYX in OK for the first X, and this cannot be continued by a single Y (because XYXYX is not possible), thus we have YXXYXXY, which can be continued by YXXYXXYY or by YXXYXXYXYY, but not by YXXYXXYXX (because this would imply an impossible 21212 in OK). However, words of the form YXYXY appear in this sequence, but they don't in A000002. - Jean-Christophe Hervé, Oct 12 2014
Applying Lenormand's "raboter" transformation (see A318921) to A000002 leads to this sequence. - Rémy Sigrist, Nov 11 2020
LINKS
Jean-Christophe Hervé, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = A000002(A078649(n)) = A000002(A078649(n)+1).
Strictly positive terms of (A000002(n)-1)*(mod(n-1, 2)+1). - Jean-Christophe Hervé, Oct 11 2014
Strictly positive terms of (1-abs(A000002(n+1)-A000002(n)))*A000002(n). - Jean-Christophe Hervé, Oct 11 2014
EXAMPLE
Kolakoski sequence begins (1),(2,2),(1,1),(2),(1),(2,2),(1),(2,2), so this one begins 2,1,2,2.
MAPLE
A156257 := proc(n)
end proc:
seq(A156257(n), n=1..50) ; # R. J. Mathar, Nov 15 2014
MATHEMATICA
OK = {1, 2, 2}; Do[OK = Join[OK, {1+Mod[n-1, 2]}], {n, 3, 1000}, {OK[[n]]}]; Select[Split[OK], Length[#] == 2&][[All, 1]] (* Jean-François Alcover, Nov 13 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 07 2009
EXTENSIONS
Definition revised by Jean-Christophe Hervé, Oct 11 2014
STATUS
approved