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

1,2

Comments

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

Links

Table of n, a(n) for n=1..70.

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).

Crossrefs

Cf. A054353, A157129.

Sequence in context: A047513 A039068 A260399 * A101616 A322678 A285137

Adjacent sequences: A229782 A229783 A229784 * A229786 A229787 A229788

Keyword

nonn

Author

Benoit Cloitre, Sep 29 2013

Status

approved