A091960 - OEIS

A091960

a(1)=1, a(2n)=a(2n-1)+(a(n)mod 2), a(2n+1)=a(2n)+1.

1, 2, 3, 3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 51, 52, 53, 54, 55, 56

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OFFSET

1,2

COMMENTS

a(4*n)=3*n iff b(2n)=0 where b(1)=1, b(2n)=(b(2n-1)+b(n)) mod 2, b(2n+1)=b(2n)+1

LINKS

Table of n, a(n) for n=1..73.

Jeffrey Shallit, Cloitre's Self-Generating Sequence, arXiv:2501.00784 [math.CO], 2025.

FORMULA

a(n) is asymptotic to (3/4)*n.

PROG

(PARI) a(n)=if(n<2, 1, if(n%2, a(n-1)+1, a(n-1)+a(n/2)%2))