OFFSET
0,25
COMMENTS
See A133500 for definition.
It is conjectured that every number converges to a fixed-point.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Full trajectories of numbers from 1 to 10000
EXAMPLE
39 -> 19683 -> 1594323 -> 38443359375 -> 59440669655040 -> 0, so a(39) = 5.
MAPLE
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;
# 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).
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;
CROSSREFS
KEYWORD
nonn,base
AUTHOR
J. H. Conway and N. J. A. Sloane, Dec 03 2007
STATUS
approved