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

1,2

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

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

Sequence in context: A066482 A324507 A123725 * A085058 A183152 A210942

Adjacent sequences: A089077 A089078 A089079 * A089081 A089082 A089083

Keyword

nonn

Author

Benoit Cloitre, Dec 04 2003

Status

approved