A216345 Position of the beginning of the n-th run in A000002.

1, 2, 4, 6, 7, 8, 10, 11, 13, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 31, 33, 34, 35, 37, 38, 40, 42, 43, 44, 46, 47, 48, 50, 51, 53, 55, 56, 58, 60, 61, 62, 64, 65, 67, 69, 70, 72, 73, 74, 76, 77, 78, 80, 82, 83, 85, 87, 88, 89, 91, 92, 94, 96, 97, 99, 101, 102, 103

Offset

1,2

Comments

If n is odd then the run is 1's, otherwise it's 2's.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

{n: A156728(n-1)=1}. - R. J. Mathar, Sep 14 2012

a(n+1) = A054353(n)+1 = a(n) + A000002(n). - Jean-Christophe Hervé, Oct 05 2014

Example

Kolakoski sequence starts 1221121 so we can see that this sequence begins 1,2,4,6,7.

Prog

(JavaScript)
a=new Array();
a[1]=1;  a[2]=2;  a[3]=2;
cd=1;  ap=3;
for (i=4; i<50; i++)
{
    if (a[ap]==1) a[i]=cd;
    else {a[i]=cd; a[i+1]=cd; i++}
    ap++;
    cd=3-cd;
}
/* document.write(a); document.write("<br>"); */
b=new Array();
b[1]=1;
c=2;
for (i=2; i<50; i++)
    if (a[i]!=a[i-1]) b[c++]=i;
document.write(b);
(Haskell)
a216345 n = a216345_list !! (n-1)
a216345_list = 1 : (filter (\x -> a000002 x /= a000002 (x - 1)) [2..])
-- Reinhard Zumkeller, Aug 03 2013

Crossrefs

Cf. A000002, A054354.

Cf. A100428, A100429.

Sequence in context: A339508 A275844 A158025 * A026510 A138204 A080645

Adjacent sequences: A216342 A216343 A216344 * A216346 A216347 A216348

Keyword

nonn

Author

Jon Perry, Sep 04 2012

Status

approved