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A003434
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Number of iterations of phi(n) needed to reach 1.
(Formerly M0244)
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22
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0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 5, 3, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 4, 5, 4, 5, 5, 6, 4, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 6, 4, 6, 5, 5, 5, 6, 5, 6, 5, 5, 6, 6, 5, 6, 6, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 5, 6, 7, 5, 7, 5, 6, 6, 7, 5, 6, 6, 6, 6, 6, 6, 7, 5, 6, 6, 7, 6, 7, 6, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Sivasankaranarayana Pillai, On a function associated with phi(n), Bull. Amer. Math. Soc., 35 (1929), 837-841.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
| By the definition of a(n) we have for n >= 2 the recursion a(n) = a(Phi(n)) + 1. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 20 2001
log_3 n << a(n) << log_2 n. [Charles R Greathouse IV, Feb 07 2012]
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EXAMPLE
| If n=164 the trajectory is {164,80,32,16,8,4,2,1}. Its length is 8, thus a(164)=7.
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MATHEMATICA
| f[n_] := Length@ NestWhileList[ EulerPhi, n, # != 1 &] - 1; Array[f, 105] (* Robert G. Wilson v, Feb 07 2012 *)
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PROG
| (PARI) A003434(n)=for(k=0, n, n>1|return(k); n=eulerphi(n)) /* Works because the loop limits are evaluated only once. Using while(...) takes 50% more time. */ [From M. F. Hasler (www.univ-ag.fr/~mhasler), Jul 01 2009]
(Haskell)
a003434 = length . takeWhile (/= 1) . (iterate a000010)
-- Reinhard Zumkeller, Jul 03 2011
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CROSSREFS
| Cf. A000010, A007755. Equals A049108 - 1.
Sequence in context: A080071 A202472 A019569 * A097849 A100678 A026834
Adjacent sequences: A003431 A003432 A003433 * A003435 A003436 A003437
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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