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A133501 Number of steps for "powertrain" operation to converge when started at n.

%I A133501 #10 Nov 26 2021 10:43:18
%S A133501 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,5,2,3,3,1,1,1,3,
%T A133501 2,5,5,5,4,9,1,1,2,5,3,3,4,6,3,5,1,1,3,2,3,5,3,3,2,4,1,1,6,3,4,4,3,3,
%U A133501 8,2,1,1,6,6,2,2,3,5,3,2,1,1,5,3,4,4,5,4,3,7,1,1,2,5,4,2,3,3,2,4,1,1,1,1,1
%N A133501 Number of steps for "powertrain" operation to converge when started at n.
%C A133501 See A133500 for definition.
%C A133501 It is conjectured that every number converges to a fixed-point.
%H A133501 N. J. A. Sloane, <a href="/A133501/b133501.txt">Table of n, a(n) for n = 0..10000</a>
%H A133501 N. J. A. Sloane, <a href="/A133501/a133501.txt">Full trajectories of numbers from 1 to 10000</a>
%e A133501 39 -> 19683 -> 1594323 -> 38443359375 -> 59440669655040 -> 0, so a(39) = 5.
%p A133501 powertrain:=proc(n) local a,i,n1,n2,t1,t2; n1:=abs(n); n2:=sign(n); t1:=convert(n1, base, 10); t2:=nops(t1); a:=1; for i from 0 to floor(t2/2)-1 do a := a*t1[t2-2*i]^t1[t2-2*i-1]; od: if t2 mod 2 = 1 then a:=a*t1[1]; fi; RETURN(n2*a); end;
%p A133501 # Compute trajectory of n under repeated application of the powertrain map of A133500. This will return -1 if the trajectory does not converge to a single number in 100 steps (so it could fail if the trajectory enters a nontrivial loop or takes longer than 100 steps to converge).
%p A133501 PTtrajectory := proc(n) local p,M,t1,t2,i; M:=100; p:=[n]; t1:=n; for i from 1 to M do t2:=powertrain(t1); if t2 = t1 then RETURN(n,i-1,p); fi; t1:=t2; p:=[op(p),t2]; od; RETURN(n,-1,p); end;
%Y A133501 For the powertrain map itself, see A133500.
%Y A133501 See A133508, A133503 for records. See A135381 for high-water marks.
%K A133501 nonn,base
%O A133501 0,25
%A A133501 _J. H. Conway_ and _N. J. A. Sloane_, Dec 03 2007