A074296 -id:A074296 - cp's OEIS frontend

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

Jon Perry, Sep 21 2002

nonn

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).

			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).

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

Cf. A074296, A074297, A074299.

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 *)

Offset corrected by Nathaniel Johnston, May 02 2011

A074297 Position of the first occurrence of n consecutive terms with the largest possible sum in the Kolakoski sequence (A000002).

Original entry on oeis.org

2, 2, 1, 6, 8, 6, 6, 2, 1, 2, 2, 1, 33, 53, 33, 6, 50, 2, 72, 74, 72, 72, 296, 295, 33, 293, 74, 324, 35, 296, 33, 35, 33, 33, 32, 2261, 30, 53, 52, 53, 53, 52, 276, 50, 33, 273, 296, 53, 296, 2883, 330, 33, 296, 295, 296, 296, 295, 33, 35, 33, 33, 32, 324, 30, 278, 35, 276

Offset: 1

Jon Perry, Sep 21 2002

nonn

The sequence of maximal sums begins 2, 4, 5, 7, 9, 10, 12, 13, 14, 16, 18, 19, 21, 23, 24, 25, 27, 28, 30, ...

			a(4)=6 because the Kolakoski sequence starting at position 6 is 2, 1, 2, 2 which sums to 7, which is the largest possible sum of 4 consecutive terms.

Hakan Icoz, Table of n, a(n) for n = 1..200

Cf. A000002, A074296, A074298.

a(8)-a(15) from and edited by Nathaniel Johnston, May 02 2011

More terms from Hakan Icoz, Jan 01 2022

cp's OEIS Frontend

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

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