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

Author

Cino Hilliard, Mar 25 2003

Keywords

• easy
• nonn

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

• Cino Hilliard, The x+1 conjecture

Crossrefs

Cf. A080791, A080800, A080801.

Programs

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" ")) ) }

Formula

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