A074292 -id:A074292 - 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).

A074293 Dominant (i.e., most populous) digit in Kolakoski sequence (A000002) when partitioned into groups of 5.

Original entry on oeis.org

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

Offset: 0

Jon Perry, Sep 21 2002

			The Kolakoski sequence begins (1,2,2,1,1), (2,1,2,2,1), (2,2,1,1,2), (1,1,2,2,1), hence sequence begins 1,2,2,1.

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Cf. A074292, A074295.

lim:=400: s:=[1,2,2]: for n from 3 to lim do for i from 1 to s[n] do s:=[op(s),1+((n-1)mod 2)]: od: od: lim2:=floor(nops(s)/5)-1: for n from 0 to lim2 do if(s[5*n+1]+s[5*n+2]+s[5*n+3]+s[5*n+4]+s[5*n+5]<=7)then printf("1, "): else printf("2, "): fi: od: # Nathaniel Johnston, May 01 2011

A156257 Digit of runs of length 2 in the Kolakoski sequence A000002: a(n) = A000002(A078649(n)).

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, 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

Benoit Cloitre, Feb 07 2009

nonn

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

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

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

Cf. A000002, A074292, A318921.

A156257 := proc(n)
    A000002(A078649(n)) ;
end proc:
seq(A156257(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]]}]; Select[Split[OK], Length[#] == 2&][[All, 1]] (* Jean-François Alcover, Nov 13 2014 *)

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

Definition revised by Jean-Christophe Hervé, Oct 11 2014

A074295 Dominant (i.e., most populous) digit in Kolakoski sequence (A000002) when partitioned into groups of 7.

Original entry on oeis.org

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

Offset: 1

Jon Perry, Sep 21 2002

			Kolakoski : (1,2,2,1,1,2,1),(2,2,1,2,2,1,1),(2,1,1,2,2,1,2),... hence 1,2,2,...

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A074292, A074293.

lim:=400: s:=[1, 2, 2]: for n from 3 to lim do for i from 1 to s[n] do s:=[op(s), 1+((n-1)mod 2)]: od: od: lim2:=floor(nops(s)/7)-1: for n from 0 to lim2 do if(add(s[7*n+k],k=1..7)<=10)then printf("1, "): else printf("2, "): fi: od: # Nathaniel Johnston, May 01 2011

A088526 a(n) = A061017(n) - pi(n) - 1.

Original entry on oeis.org

0, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2

Offset: 1

David Applegate and N. J. A. Sloane, Oct 22 2008

sign

a(n) >= 0 for all n >= 24.

The old entry with this sequence number was a duplicate of A074292.

Cf. A061017, A006218, A098357, A052511.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

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

Views

Author

Keywords

Comments

Links

Crossrefs

A074293 Dominant (i.e., most populous) digit in Kolakoski sequence (A000002) when partitioned into groups of 5.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A156257 Digit of runs of length 2 in the Kolakoski sequence A000002: a(n) = A000002(A078649(n)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A074295 Dominant (i.e., most populous) digit in Kolakoski sequence (A000002) when partitioned into groups of 7.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A088526 a(n) = A061017(n) - pi(n) - 1.

Views

Author

Keywords

Comments

Crossrefs