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A039650
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Prime reached by iterating f(x) = phi(x)+1 on n.
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15
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2, 2, 3, 3, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 7, 7, 17, 7, 19, 7, 13, 11, 23, 7, 13, 13, 19, 13, 29, 7, 31, 17, 13, 17, 13, 13, 37, 19, 13, 17, 41, 13, 43, 13, 13, 23, 47, 17, 43, 13, 13, 13, 53, 19, 41, 13, 37, 29, 59, 17, 61, 31, 37, 13, 43, 13, 67, 13, 13, 13, 71, 13, 73, 37, 41
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OFFSET
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1,1
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COMMENTS
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Or, a(n) = lim_k {s(k,n)} where s(k,n) is defined inductively on k by: s(1,n) = n; s(k+1,n) = 1 + phi(s(k,n)). - Joseph L. Pe, Apr 30 2002
Sequence A229487 gives the conjectured largest number that converges to prime(n). - T. D. Noe, Oct 17 2013
For n>1, phi(n) <= n-1, with equality iff n is prime. So the trajectory decreases until it hits a prime. So a(n) always exists. - N. J. A. Sloane, Sep 22 2017
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REFERENCES
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Alexander S. Karpenko, Lukasiewicz Logics and Prime Numbers, Luniver Press, Beckington, 2006, p. 51.
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LINKS
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EXAMPLE
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s(24,1) = 24, s(24,2) = 1 + phi(24) = 1 + 8 = 9, s(24,3) = 1 + phi(9) = 1 + 6 = 7, s(24,4) = 1 + phi(7) = 1 + 6 = 7,.... Therefore a(24) = lim_k {s(24,k)} = 7.
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MAPLE
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local nitr, niitr ;
niitr := n ;
while true do:
nitr := 1+numtheory[phi](niitr) ;
if nitr = niitr then
return nitr ;
end if;
niitr := nitr ;
end do:
end proc:
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MATHEMATICA
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f[n_] := FixedPoint[1 + EulerPhi[ # ] &, n]; Table[ f[n], {n, 1, 75}]
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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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