A232014 Number of iterations of A032445 ("position of n in Pi") until a value is reached for the second time, when starting with n, or -1 if no value is repeated.

16, 4, 3, 5, 6, 1

Offset

0,1

Comments

See A232013 for a variant based on A176341 instead of A032445.

Some loops: (5), (271070), (9292071), (40, 71), (2, 7, 14), (296, 1060, 13737, 133453, 646539, 294342, 141273). - Hans Havermann, Jul 26 2014

See Hans Havermann table (in links) for primary unknown-length evolutions. - Hans Havermann, Aug 06 2014

Links

Table of n, a(n) for n=0..5.

David G. Andersen, Loop Sequences within Pi, on The Pi-Search Page (Search 2*10^8 decimal digits of Pi).

Hans Havermann, Information table of n, a(n) for n=0..100.

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

James Taylor, Irrational Numbers Search Engine (Search 2*10^9 decimal digits of Pi).

Ady Tzidon, Loops in Pi.

Example

a(1)=4 since A032445(1)=2 (the first "1" occurs after the initial "3" as second digit in Pi), A032445(2)=7 (the first "2" occurs as 7th digit of Pi's decimal expansion), A032445(7)=14, A032445(14)=2, which "closes the loop" after 4 iterations. (The initial value does not need to be part of the loop.)

Prog

(PARI) A232014(n)={my(u=0); for(i=1, 9e9, u+=1<<n; bittest(u, n=A032445(n))&&return(i))}

Crossrefs

Cf. A032445.

Sequence in context: A040246 A075462 A082959 * A018814 A307407 A234288

Adjacent sequences: A232011 A232012 A232013 * A232015 A232016 A232017

Keyword

nonn,base,more

Author

M. F. Hasler, Nov 16 2013

Extensions

Definition modified by N. J. A. Sloane, Jul 29 2014

Status

approved