A074298 First occurrence of an 'average' valued sequence of length 2n in the Kolakoski sequence (A000002).

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 9, 4, 4, 3, 1, 4, 3, 1, 1, 9, 4, 4, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 3, 1, 1, 4, 3

Offset

1,6

Comments

a(n) is the least k such that K(k) + K(k+1) + ... + K(k + 2*n - 1) = 3*n, where K(m) = A000002(m).

Links

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

Example

a[1]=1, as A000002 begins 1,2 (sum 3) a[2]=1, as A000002 begins 1,2,2,1 (sum 6) a[3]=1, as A000002 begins 1,2,2,1,1,2 (sum 9).

Mathematica

nmax = 90; a2 = {1, 2, 2}; For[n = 3, n <= 2*nmax, n++, For[i = 1, i <= a2[[n]], i++, AppendTo[a2, 1 + Mod[n - 1, 2]]]]; a[n_] := For[k = 1, True, k++, If[Plus @@ a2[[k ;; k + 2*n - 1]] == 3*n, Return[k]]]; Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Sep 25 2012 *)

Crossrefs

Cf. A074296, A074297, A074299.

Sequence in context: A030558 A030557 A086997 * A356097 A356096 A326029

Adjacent sequences: A074295 A074296 A074297 * A074299 A074300 A074301

Keyword

nonn

Author

Jon Perry, Sep 21 2002

Extensions

Offset corrected by Nathaniel Johnston, May 02 2011

Status

approved