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

0,3

Comments

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

Links

Table of n, a(n) for n=0..7.

J. Navarro, Les secrets du nombre Pi (Book review, in French).

Pi-Search Page, Loop Sequences within Pi.

Ady TZIDON, Loops in Pi.

Example

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.

Prog

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

Crossrefs

Cf. A176341, A232013, A232014, A032445.

Sequence in context: A019937 A176460 A320378 * A260947 A070489 A112268

Adjacent sequences: A228409 A228410 A228411 * A228413 A228414 A228415

Keyword

nonn,base,more

Author

M. F. Hasler, Nov 16 2013

Status

approved