

A061436


Number of steps for trajectory of n to reach 1 under the map that sends x > x/3 if x mod 3 = 0, x > x+3(x mod 3) if x is not 0 mod 3 (for a 2nd time when n starts at 1).


1



2, 2, 1, 4, 4, 3, 3, 3, 2, 6, 6, 5, 6, 6, 5, 5, 5, 4, 5, 5, 4, 5, 5, 4, 4, 4, 3, 8, 8, 7, 8, 8, 7, 7, 7, 6, 8, 8, 7, 8, 8, 7, 7, 7, 6, 7, 7, 6, 7, 7, 6, 6, 6, 5, 7, 7, 6, 7, 7, 6, 6, 6, 5, 7, 7, 6, 7, 7, 6, 6, 6, 5, 6, 6, 5, 6, 6, 5, 5, 5, 4, 10, 10, 9, 10, 10, 9, 9, 9, 8, 10, 10, 9, 10, 10, 9, 9, 9, 8, 9, 9
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OFFSET

1,1


COMMENTS

This sequence is generated by the pari program below for m=3,p=1. Other values of m and p also converge but not necessarily to 1. For m =2 and p=1 we have the count of steps for the x+1 problem. m=prime and p=m+1 usually converge to 1 but break down for certain values of n. E.g. 17 locks at n=34, 23 at n=49 29 at n=91. I verified m=7 for n up to 100000. 100000 requires 157 steps to reach 1.


LINKS

Table of n, a(n) for n=1..101.
Cino Hilliard, The x+1 conjecture


EXAMPLE

x = 1. step1:x=1+31=3 step2: x=3/3=1. Count =2 steps.


PROG

(PARI) multxp2(n, m, p) = { print1(2" "); for(j=1, n, x=j; c=0; while(x>1, r = x%m; if(r==0, x=x/m, x=x*p+mr); print1(x" "); ); ) }


CROSSREFS

Sequence in context: A110664 A193922 A319534 * A214095 A213948 A136787
Adjacent sequences: A061433 A061434 A061435 * A061437 A061438 A061439


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Mar 29 2003


STATUS

approved



