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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).
2
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
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
KEYWORD
nonn
AUTHOR
Jon Perry, Sep 21 2002
EXTENSIONS
Edited by Nathaniel Johnston, May 02 2011
STATUS
approved