

A089080


Sequence is S(infinity) where S(1)={1,2} and S(n)=S(n1)S'(n1), where S'(k) is obtained from S(k) by replacing the single 1 with the least integer not occurring in S(k).


4



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
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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(n2)); \\ Antti Karttunen, Nov 01 2018


CROSSREFS

Essentially the same as A085058 (with prepended 1 and different indexing).
Sequence in context: A199968 A066482 A123725 * A085058 A183152 A210942
Adjacent sequences: A089077 A089078 A089079 * A089081 A089082 A089083


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Dec 04 2003


STATUS

approved



