A156257 -id:A156257 - cp's OEIS frontend

A248805 The difference A156257(n)-A074292(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Jean-Christophe Hervé, Oct 11 2014

sign

Related to the position and frequency of runs of length 2 in the Kolakoski sequence A000002.

Possible values are -1, 0, 1, and a 1 seems to be always followed soon by a -1, indicating that the two sequences A074292 and A156257 are not equal but rather close (this might help to show the equality of the proportions of 1 and 2 in the Kolakoski sequence).

Jean-Christophe Hervé, Table of n, a(n) for n = 1..5000

Cf. A000002, A074292, A156257.

A248805 := proc(n)
    A156257(n)-A074292(n) ;
end proc:
seq(A248805(n),n=1..80) ; # R. J. Mathar, Nov 15 2014

A249372 Numbers k such that A156257(k) != A074292(k).

Original entry on oeis.org

47, 48, 56, 57, 128, 129, 137, 139, 147, 148, 176, 177, 182, 183, 185, 187, 188, 190, 192, 194, 195, 196, 197, 199, 201, 202, 203, 205, 207, 209, 210, 211, 212, 214, 218, 220, 222, 223, 227, 229, 230, 232, 233, 235, 237, 238, 239, 240, 242, 244

Offset: 1

Jean-Christophe Hervé, Nov 22 2014

nonn

Related to the position and frequency of runs of length 2 in the Kolakoski sequence A000002. Possible values of the difference A156257 - A074292 are -1, 0, 1, and a 1 seems to be always followed soon by a -1, indicating that the two sequences A074292 and A156257 are not equal but rather close.

Jean-Christophe Hervé, Table of n, a(n) for n = 1..49383

Cf. A000002, A074292, A156257, A247176 (values of the difference).

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

Original entry on oeis.org

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, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 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

Offset: 1

Jon Perry, Sep 21 2002

nonn

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.
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
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

			Kolakoski begins (1,2,2), (1,1,2), (1,2,2), (1,2,2), so this begins 2,1,2,2.

Nathaniel Johnston, Table of n, a(n) for n = 1..10001
Claude Lenormand, Deux transformations sur les mots, 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

Cf. A000002, A074293, A074295, A156257, A248805, A318921.

A074292 := proc(n)
    A000002(3*n-2)+A000002(3*n-1)+A000002(3*n)-3 ;
end proc:
seq(A074292(n),n=1..50) ; # R. J. Mathar, Nov 15 2014

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 *)

a(n)=A000002(3n-2)+A000002(3n-1)+A000002(3n)-3. - Benoit Cloitre, Nov 15 2003

More terms from Ray Chandler, Nov 16 2003

Offset corrected by Jean-Christophe Hervé, Oct 11 2014

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A248805 The difference A156257(n)-A074292(n).

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A249372 Numbers k such that A156257(k) != A074292(k).

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

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