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A133501 Number of steps for "powertrain" operation to converge when started at n. 17
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
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

See A133508, A133503 for records. See A135381 for high-water marks.

Sequence in context: A108053 A327969 A328324 * A254176 A257090 A124316

Adjacent sequences:  A133498 A133499 A133500 * A133502 A133503 A133504

KEYWORD

nonn,base

AUTHOR

J. H. Conway and N. J. A. Sloane, Dec 03 2007

STATUS

approved

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Last modified April 6 02:20 EDT 2020. Contains 333267 sequences. (Running on oeis4.)