

A232013


Number of iterations of A176341 ("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.


6




OFFSET

0,1


COMMENTS

See A232014 for a variant based on A032445 instead of A176341.
Some loops: (1), (711939213), (0, 32, 15, 3), (19, 37, 46), (40, 70, 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169).
See Hans Havermann table (in links) for primary unknownlength evolutions.


LINKS

Table of n, a(n) for n=0..7.
David G. Andersen, Loop Sequences within Pi, on The PiSearch 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(0)=4 since A176341(0)=32 (position of the first "0" in Pi's digits), A176341(32)=15 (position of the first "32" in Pi's digits), A176341(15)=3 (position of the first "15" in Pi's digits), A176341(3)=0 (position of the first "3" in Pi's digits); here we find the "0" again after 4 iterations, thus a(0)=4.
a(1)=1 since A176341(1)=1 (the first "1" occurs at position 1 in Pi's digits), which already "closes the loop" after 1 iteration.
a(2)=12 because the iterations yield 2 > 6 > 7 > 13 > 110 > 174 > 155 > 314 > 0 > 32 > 15 > 3 > 0, here we reenter the loop (of length 4) after 12 iterations.


PROG

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


CROSSREFS

Sequence in context: A130322 A316232 A212046 * A246943 A106194 A272099
Adjacent sequences: A232010 A232011 A232012 * A232014 A232015 A232016


KEYWORD

nonn,base,more


AUTHOR

M. F. Hasler, Nov 16 2013


EXTENSIONS

Edited by Hans Havermann, Aug 01 2014


STATUS

approved



