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A076773 2-nadirs of phi: numbers k such that phi(k-2) > phi(k-1) > phi(k) < phi(k+1) < phi(k+2).

%I A076773 #19 Sep 08 2022 08:45:07
%S A076773 315,525,735,1155,1365,1575,1755,1785,1815,1995,2145,2415,2475,2805,
%T A076773 3045,3315,3465,3885,4095,4125,4305,4515,4725,4935,5115,5145,5355,
%U A076773 5775,6045,6195,6405,6435,6615,6825,7035,7095,7245,7395,7455,7605,7665,8085
%N A076773 2-nadirs of phi: numbers k such that phi(k-2) > phi(k-1) > phi(k) < phi(k+1) < phi(k+2).
%C A076773 I call n a "k-nadir" (or nadir of depth k) of the arithmetical function f if n satisfies f(n-k) > ... > f(n-1) > f(n) < f(n+1) < ... < f(n+k).
%C A076773 If just phi(n-1) > phi(n) < phi(n+1) is required for odd n, does this lead to a different sequence? That is, are there consecutive odd numbers in A161962 or consecutive even numbers in A161963? - _Jianing Song_, Jan 12 2019
%H A076773 Amiram Eldar, <a href="/A076773/b076773.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from G. C. Greubel)
%e A076773 phi(313), ..., phi(317) equal 312, 156, 144, 156, 316, respectively, so 315 is a 2-nadir of phi(n).
%t A076773 Select[Range[3, 10^4], EulerPhi[#-2] > EulerPhi[#-1] > EulerPhi[#] < EulerPhi[#+1] < EulerPhi[#+2] &]
%o A076773 (Sage) [n for n in (3..9000) if euler_phi(n-2) > euler_phi(n-1) > euler_phi(n) < euler_phi(n+1) < euler_phi(n+2)] # _G. C. Greubel_, Feb 27 2019
%o A076773 (Magma) eu:=EulerPhi; f:=func<n|eu(n) lt eu(n+1) and eu(n+1) lt eu(n+2)>; f1:= func<n|eu(n) lt eu(n-1) and eu(n-1) lt eu(n-2)>; [k:k in [3..8100]|f(k) and f1(k)]; // _Marius A. Burtea_, Feb 19 2020
%Y A076773 Cf. A000010, A161962, A161963.
%K A076773 nonn
%O A076773 1,1
%A A076773 _Joseph L. Pe_, Nov 14 2002