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A227944
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Number of iterations of "take odd part of phi" (A053575) to reach 1 from n.
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11
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0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 3, 2, 2, 3, 4, 1, 3, 2, 1, 2, 3, 3, 2, 2, 3, 3, 4, 1, 2, 2, 3, 1, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 1, 4, 2, 3, 2, 1, 3, 3, 2, 3, 2, 3, 3, 2, 4, 3, 1, 2, 3, 2, 2
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OFFSET
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1,7
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COMMENTS
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LINKS
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FORMULA
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For n > 1, a(n) = a(A053575(n)) + 1.
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EXAMPLE
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a(18) = 2 because it takes two steps to reach 1 from 18: phi(18) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
a(19) = 3 because it takes three steps to reach 1 from 19: phi(19) = 18, the odd part of which is 9, and phi(9) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
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MATHEMATICA
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oddPhi[n_] := Module[{phi = EulerPhi[n]}, phi/2^IntegerExponent[phi, 2]]; Table[Length[NestWhileList[oddPhi[#] &, n, # > 1 &]] - 1, {n, 100}] (* T. D. Noe, Oct 07 2013 *)
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PROG
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(Haskell)
a227944 n = fst $
until ((== 1) . snd) (\(i, x) -> (i + 1, a053575 x)) (0, n)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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