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

Author

M. F. Hasler, Nov 16 2013

Keywords

• nonn
• base
• more

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

Examples

			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.)
		

Links

• 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.

Crossrefs

Cf. A032445.

Programs

PARI

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

Extensions

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