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

Author

Jon Perry, Sep 21 2002

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A074298, A022292

Programs

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("
"); */
function isElement(x, arr)
{
    for (j=1; jx) return false;
    }
    return false;
}
for (i=1; i<500; i++)
    if (!isElement(2*i, b))
        document.write(2*i+", ");
// Jon Perry, Sep 11 2012

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 *)

Extensions

Edited by Nathaniel Johnston, May 02 2011