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A340762 Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 4, 2, 1.

%I A340762 #29 Dec 22 2024 15:58:22
%S A340762 4,5,8,10,11,12,13,15,16,17,20,21,22,23,24,25,26,28,29,30,31,32,33,34,
%T A340762 35,36,37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,55,56,57,58,59,
%U A340762 60,61,62,63,64,65,66,67,68,69,70,71,72
%N A340762 Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 4, 2, 1.
%C A340762 Infinite set (see reference).
%H A340762 Robert Israel, <a href="/A340762/b340762.txt">Table of n, a(n) for n = 1..10000</a>
%H A340762 Eliot T. Jacobson and Alan E. Parks, <a href="https://www.jstor.org/stable/2323032?seq=1">Infinite branches of the phi-tree</a>, Amer. Math. Monthly, Vol. 93, No. 7 (August-September 1986), pp. 552-554.
%H A340762 Keith Matthews, <a href="http://www.numbertheory.org/php/carmichael.html">Solving phi(x)=n, where phi(x) is Euler's totient function</a>.
%e A340762 11 is in the list because phi(phi(11)) = phi(10) = 4.
%p A340762 filter:= proc(n) option remember;
%p A340762   if n < 4 then false
%p A340762   elif n = 4 then true
%p A340762   else procname(numtheory:-phi(n))
%p A340762   fi
%p A340762 end proc:
%p A340762 select(filter, [$4..100]); # _Robert Israel_, Dec 23 2021
%t A340762 Select[Range[4, 72], FixedPointList[EulerPhi, #][[-4]] == 4 &] (* _Amiram Eldar_, Jan 27 2021 *)
%o A340762 (PARI) isok(k) = if (k>=4, while((k!=6) && (k!=4), k=eulerphi(k))); k == 4; \\ _Michel Marcus_, Feb 01 2021
%Y A340762 Cf. A000010, A340765 (complement relative to {n>=4}).
%Y A340762 Cf. A003434, A032358, A049108.
%K A340762 nonn
%O A340762 1,1
%A A340762 _Franz Vrabec_, Jan 20 2021