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A254411 Limit of f(f(f(...f(0)...))) modulo n as the number of iterations of f(x) = 2^x+1 grows.

%I A254411 #22 Mar 01 2025 01:26:51
%S A254411 0,1,0,1,3,3,2,1,0,3,9,9,6,9,3,1,3,9,0,13,9,9,7,9,18,19,0,9,20,3,9,1,
%T A254411 9,3,23,9,32,19,6,33,34,9,40,9,18,7,35,33,23,43,3,45,42,27,53,9,0,49,
%U A254411 32,33,54,9,9,1,58,9,44,37,30,23,30,9,2,69,18,57,9,45,65,33,0,75,25,9,3,83,78,9,68,63,58,53,9,35,38,33,71,23,9,93
%N A254411 Limit of f(f(f(...f(0)...))) modulo n as the number of iterations of f(x) = 2^x+1 grows.
%C A254411 Also, limit of f(f(f(...f(m)...))) modulo n for any integer m >= 0.
%H A254411 Rémy Sigrist, <a href="/A254411/b254411.txt">Table of n, a(n) for n = 1..10000</a>
%F A254411 a(n) = limit of A254429(m) mod n as m grows.
%F A254411 a(n) = A254429(A227944(n)+k) mod n for any k>=1. In particular, a(n) = A254429(n) mod n.
%o A254411 (PARI) { A254411(m) = my(g); if(m==1, return(0)); g=2^valuation(m,2); m\=g; lift( chinese(Mod(0,g),Mod(2,m)^A254411(eulerphi(m)) ) + 1) }
%Y A254411 Cf. A245970, A254410.
%K A254411 nonn,easy,nice,look
%O A254411 1,5
%A A254411 _Max Alekseyev_, Jan 30 2015