

A080799


Number of divide by 2 and add 1 operations required to reach ...,7,8,4,2,1 when started at n.


2



6, 5, 8, 7, 7, 6, 10, 9, 9, 8, 9, 8, 8, 7, 12, 11, 11, 10, 11, 10, 10, 9, 11, 10, 10, 9, 10, 9, 9, 8, 14, 13, 13, 12, 13, 12, 12, 11, 13, 12, 12, 11, 12, 11, 11, 10, 13, 12, 12, 11, 12, 11, 11, 10, 12, 11, 11, 10, 11, 10, 10, 9, 16, 15, 15, 14, 15, 14, 14, 13, 15, 14, 14, 13, 14, 13, 13
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OFFSET

1,1


COMMENTS

More precisely, number of steps to reach 1 but passing through 7 first.
A 3x+1  type sequence cannot contain ..., 7, 8, 4, 2, 1 because 7 is odd and the recurrence will always yield 22 as the number that follows 7. So the x+1 conjecture has a property the 3x+1 conjecture does not have. The link will allow you to try very large numbers for these conjectures.


LINKS

Table of n, a(n) for n=1..77.
Cino Hilliard, The x+1 conjecture


FORMULA

a(n) = A023416(n+1) + floor(log_2(n+1)) + 4.  Ralf Stephan, Mar 03 2004


PROG

(PARI) xpcount2(n, p) = { for(x=1, n, p1 = x; f=0; ct=0; while(p1>1, if(p1%2==0, p1/=2; ct++, p1 = p1*p+1; ct++); if(p1==7, p2=7; if(p2%2==0, p2/=2, p2 = p2*p+1); if(p2 ==8 && p1 ==7, f=1) ); ); if(f, print1(ct" ")) ) }


CROSSREFS

Cf. A080791, A080800, A080801.
Sequence in context: A253300 A339253 A335165 * A262512 A272696 A048236
Adjacent sequences: A080796 A080797 A080798 * A080800 A080801 A080802


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Mar 25 2003


STATUS

approved



