A228412 Number of iterations of A176341 ("position of m in Pi") starting with n until a loop is reached.

0, 0, 8, 0, 9, 10, 7, 6

Offset: 0

Author

M. F. Hasler, Nov 16 2013

Keywords

• nonn
• base
• more

Comments

"A loop is reached" means that an element x is reached such that (A176341^k)(x) = x for some k>0.

Examples

			a(0)=a(1)=a(3)=0 since 0 and 3 are elements of the loop 0 -> 32 -> 15 -> 3 -> 0, and 1 is a fixed point (i.e., loop of length 1) of A176341.
a(2)=8 is the number of steps in 2 -> 6 -> 7 -> 13 -> 110 -> 174 -> 155 -> 314 -> 0, at which point the previously mentioned loop is reached.
		

Links

• J. Navarro, Les secrets du nombre Pi (Book review, in French).
• Pi-Search Page, Loop Sequences within Pi.
• Ady TZIDON, Loops in Pi.

Crossrefs

Cf. A176341, A232013, A232014, A032445.

Programs

PARI

A228412(n)={my(u=0);for(i=1,9e9,u+=1<A176341(n))&&return(i-A232013(n)))}