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A228412 Number of iterations of A176341 ("position of m in Pi") starting with n until a loop is reached.

%I A228412 #22 Oct 19 2024 15:57:32
%S A228412 0,0,8,0,9,10,7,6
%N A228412 Number of iterations of A176341 ("position of m in Pi") starting with n until a loop is reached.
%C A228412 "A loop is reached" means that an element x is reached such that (A176341^k)(x) = x for some k>0.
%H A228412 J. 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 A228412 Pi-Search Page, <a href="http://www.angio.net/pi">Loop Sequences within Pi</a>.
%H A228412 Ady TZIDON, <a href="http://perplexus.info/show.php?pid=7746&amp;op=sol">Loops in Pi</a>.
%e A228412 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.
%e A228412 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.
%o A228412 (PARI) A228412(n)={my(u=0);for(i=1,9e9,u+=1<<n;bittest(u,n=A176341(n))&&return(i-A232013(n)))}
%Y A228412 Cf. A176341, A232013, A232014, A032445.
%K A228412 nonn,base,more
%O A228412 0,3
%A A228412 _M. F. Hasler_, Nov 16 2013