A080799 Number of divide by 2 and add 1 operations required to reach ...,7,8,4,2,1 when started at n.

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

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 A348909 A272696

Adjacent sequences: A080796 A080797 A080798 * A080800 A080801 A080802

Keyword

easy,nonn

Author

Cino Hilliard, Mar 25 2003

Status

approved