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A133501 Number of steps for "powertrain" operation to converge when started at n. 7
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: A241476 A195719 A108053 * 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 July 26 18:35 EDT 2017. Contains 289839 sequences.