A089080 Sequence is S(infinity) where S(1)={1,2} and S(n)=S(n-1)S'(n-1), where S'(k) is obtained from S(k) by replacing the single 1 with the least integer not occurring in S(k).

1, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 7, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 8, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 7, 2, 3, 2, 4, 2, 3, 2, 5

Offset: 1

Author

Benoit Cloitre, Dec 04 2003

Keywords

• nonn
• easy

Examples

			S(1)={1,2} then S'(1)={3,2} and sequence begins 1,2,3,2
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Essentially the same as A085058 (with prepended 1 and different indexing).

Cf. A094267 (first differences), A208147 (partial products).

Programs

PARI

A085058(n) = (valuation(n+1, 2)+2);
A089080(n) = if(1==n,n,A085058(n-2)); \\ Antti Karttunen, Nov 01 2018

Formula

Sum_{k=1..n} a(k) = 3*n+O(log(n)) ( Sum_{k=1..n} a(k) < 3*n )