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A328056 Numbers k such that phi(k) > phi(k+1) > phi(k+2) where phi is the Euler totient function (A000010).

%I A328056 #22 Sep 08 2022 08:46:24
%S A328056 313,523,733,823,824,943,944,973,1153,1363,1573,1753,1783,1813,1993,
%T A328056 2143,2413,2473,2623,2803,3043,3133,3134,3253,3313,3463,3703,3883,
%U A328056 4093,4123,4303,4387,4388,4513,4723,4873,4874,4933,5113,5143,5353,5443,5444,5563,5564
%N A328056 Numbers k such that phi(k) > phi(k+1) > phi(k+2) where phi is the Euler totient function (A000010).
%C A328056 Contains all members k of A206581 such that k==103 (mod 210) except 103.- _Robert Israel_, Oct 16 2019
%H A328056 Robert Israel, <a href="/A328056/b328056.txt">Table of n, a(n) for n = 1..10000</a>
%e A328056 313 is in the sequence since phi(313) = 312, phi(314) = 156, phi(315) = 144, and 312 > 156 > 144.
%p A328056 R:= NULL: count:= 0:
%p A328056 q:= false: s:= 0:
%p A328056 for i from 1 while count < 100 do
%p A328056   t:= numtheory:-phi(i);
%p A328056   r:= q;
%p A328056   q:= evalb(t<s);
%p A328056   if r and q then count:= count+1; R:= R, i-2 fi;
%p A328056   s:= t;
%p A328056 od:
%p A328056 R; # _Robert Israel_, Oct 16 2019
%t A328056 Flatten[Position[Partition[EulerPhi[Range[5600]], 3, 1], _?(Max[Differences[#]] < 0 &)] // Quiet] (* _Amiram Eldar_, Oct 06 2019 after _Harvey P. Dale_ at A078776 *)
%o A328056 (Magma) [k:k in [1..5600]| EulerPhi(k) gt EulerPhi(k+1) and EulerPhi(k+1) gt EulerPhi(k+2)]; // _Marius A. Burtea_, Oct 07 2019
%Y A328056 Cf. A000010, A078776, A161962, A161963, A206581, A327880.
%Y A328056 Supersequence of A326817.
%K A328056 nonn
%O A328056 1,1
%A A328056 _Kritsada Moomuang_, Oct 03 2019