A229785 - OEIS

%I #9 Sep 29 2013 21:18:03

%S 1,2,4,6,7,8,9,10,12,14,16,18,19,20,22,24,25,26,28,30,31,32,33,34,36,

%T 38,40,42,43,44,45,46,48,50,52,54,55,56,58,60,61,62,63,64,66,68,70,72,

%U 73,74,76,78,79,80,81,82,84,86,88,90,91,92,94,96,97,98,100,102,103,104

%N Partial sums of A157129.

%C Although the behavior of the partial sums of the Kolakoski sequence (A054353) is mysterious, this sequence is much easier to handle.

%F a(n)=(3/2)n+O(1). More precisely, let b(n)=3*n-2*a(n); then b(n) satisfies the following recurrence modulo 12: b(n)=1,2,1,0,1,2,3,4,3,2,1 for n=1,2,3,4,5,6,7,8,9,10,11. Then for k>=1 we have b(12k)=b(4k), b(12k+1)=b(4k+1), b(12k+2)=b(4k+2), b(12k+2)=b(4k+2), b(12k+3)=b(4k+2)-1, b(12k+4)=b(4k+2)-2, b(12k+5)=b(4k+2)-1, b(12k+6)=b(4k+2), b(12k+7)=4-b(4k+3), b(12k+8)=4-b(4k+4), b(12k+9)=4-b(4k+3), b(12k+10)=4-b(4k+2), b(12k+11)=b(4k+3).

%Y Cf. A054353, A157129.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Sep 29 2013