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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 16:06 EST 2023. Contains 360128 sequences. (Running on oeis4.)