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A072086
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Number of steps to reach 1, starting with n and applying the A072084-map repeatedly.
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3
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0, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 2, 3, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 1, 3, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 3, 3, 3, 2
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OFFSET
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1,3
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LINKS
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EXAMPLE
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n=21: '11'*'111' -> '10'*'11' -> '11'*'1' -> '1'; i.e., 21=3*7 -> 6=2*3 -> 2*1 -> 1*1=1, therefore a(21)=3.
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MAPLE
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A072086 := proc(n) local c, i, j; c :=0; i := n;
while i > 1 do i:=A072084(i); c:=c+1 od; c end:
# Note that this gives A072086(0)=0 if desired
# without any additional case discrimination.
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MATHEMATICA
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b[1] = 1; b[n_] := Times @@ Power @@@ (FactorInteger[n] /. {p_Integer, e_} :> {DigitCount[p, 2, 1], e}); a[n_] := Length[FixedPointList[b, n]] - 2; Array[a, 100] (* Jean-François Alcover, Feb 09 2018 *)
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PROG
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(Haskell)
a072086 n = fst $
until ((== 1) . snd) (\(i, x) -> (i + 1, a072084 x)) (0, n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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