cp's OEIS Frontend

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.

%I A232014 #39 Oct 19 2024 15:57:32
%S A232014 16,4,3,5,6,1
%N 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.
%C A232014 See A232013 for a variant based on A176341 instead of A032445.
%C A232014 Some loops: (5), (271070), (9292071), (40, 71), (2, 7, 14), (296, 1060, 13737, 133453, 646539, 294342, 141273). - _Hans Havermann_, Jul 26 2014
%C A232014 See Hans Havermann table (in links) for primary unknown-length evolutions. - _Hans Havermann_, Aug 06 2014
%H A232014 David G. Andersen, <a href="http://www.angio.net/pi">Loop Sequences within Pi, on The Pi-Search Page</a> (Search 2*10^8 decimal digits of Pi).
%H A232014 Hans Havermann, <a href="http://chesswanks.com/seq/a232014.txt">Information table of n, a(n) for n=0..100</a>.
%H A232014 Joaquin Navarro, <a href="http://images-archive.math.cnrs.fr/Les-secrets-du-nombre-Pi.html">Les secrets du nombre Pi</a> (Book review, in French).
%H A232014 James Taylor, <a href="http://www.subidiom.com/pi/">Irrational Numbers Search Engine</a> (Search 2*10^9 decimal digits of Pi).
%H A232014 Ady Tzidon, <a href="http://perplexus.info/show.php?pid=7746&amp;op=sol">Loops in Pi</a>.
%e A232014 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.)
%o A232014 (PARI) A232014(n)={my(u=0);for(i=1,9e9,u+=1<<n;bittest(u,n=A032445(n))&&return(i))}
%Y A232014 Cf. A032445.
%K A232014 nonn,base,more
%O A232014 0,1
%A A232014 _M. F. Hasler_, Nov 16 2013
%E A232014 Definition modified by _N. J. A. Sloane_, Jul 29 2014