A074299 Lengths of subsequences such that the first 'average' value (a[n]*1.5) is not achieved from the starting position in the Kolakoski sequence (A000002).

12, 32, 34, 52, 66, 84, 90, 92, 94, 96, 100, 102, 108, 110, 112, 114, 120, 134, 154, 156, 166, 172, 174, 194, 196, 202, 216, 230, 248, 254, 256, 258, 260, 266, 268, 272, 274, 276, 278, 280, 284, 286, 292, 294, 296, 298, 304, 318, 336, 342, 344, 348, 350, 352

Offset

1,1

Comments

All members of this sequence are even. 2n is in this sequence if and only if A074298(n)>1.

The even numbers missing from A022292.

Links

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

Example

The initial run of 12 adds up to 19, however if we start at position 3, then the sum is 18.

Mathematica

max = 200; kol = {1, 2, 2}; For[n=3, n <= 2*max, n++, For[i=1, i <= kol[[n]], i++, AppendTo[kol, 1 + Mod[n-1, 2]]]]; A074298[n_] := For[k=1, True, k++, If[Plus @@ kol[[k ;; k + 2*n - 1]] == 3*n, Return[k]]]; Select[2*Range[max], A074298[#/2] > 1 &] (* Jean-François Alcover, Sep 25 2012 *)

Prog

(JavaScript)
a=new Array();
a[1]=1; a[2]=2; a[3]=2; cd=1; ap=3;
for (i=4; i<1000; i++)
{
    if (a[ap]==1) a[i]=cd;
    else {a[i]=cd; a[i+1]=cd; i++}
    ap++;
    cd=3-cd;
}
b=new Array();
oc=0; tc=0; c=1;
for (i=1; i<1000; i++)
{
    if (oc==tc) b[c++]=i-1;
    if (a[i]==1) oc++;
    else tc++;
}
/* document.write(b); */
/* document.write("<br>"); */
function isElement(x, arr)
{
    for (j=1; j<arr.length; j++)
    {
        if (arr[j]==x) return true;
        if (arr[j]>x) return false;
    }
    return false;
}
for (i=1; i<500; i++)
    if (!isElement(2*i, b))
        document.write(2*i+", ");
// Jon Perry, Sep 11 2012

Crossrefs

Cf. A074298, A022292

Sequence in context: A038624 A302362 A262239 * A118528 A031118 A335100

Adjacent sequences: A074296 A074297 A074298 * A074300 A074301 A074302

Keyword

nonn

Author

Jon Perry, Sep 21 2002

Extensions

Edited by Nathaniel Johnston, May 02 2011

Status

approved