A229785 Partial sums of A157129.

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, 38, 40, 42, 43, 44, 45, 46, 48, 50, 52, 54, 55, 56, 58, 60, 61, 62, 63, 64, 66, 68, 70, 72, 73, 74, 76, 78, 79, 80, 81, 82, 84, 86, 88, 90, 91, 92, 94, 96, 97, 98, 100, 102, 103, 104

Offset: 1

Author

Benoit Cloitre, Sep 29 2013

Keywords

• nonn

Comments

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

Crossrefs

Cf. A054353, A157129.

Formula

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).