|
%I #22 Sep 08 2022 08:45:07
%S 1,5,7,11,17,22,88,292,847,1337,1691,7367,10385,15430,51215,93401,
%T 132535,211817,282725,358852,359905,382955,486772,507725,580262,
%U 664870,700532,1691081,1972691,2637712,5154625,5886265,6510485,13841531
%N Numbers k such that phi(k) + phi(k+3) = phi(k+1) + phi(k+2).
%C Each term of the sequence marks the start of four consecutive phi-values for which the sum of the means equals the sum of the extremes.
%H Amiram Eldar, <a href="/A076665/b076665.txt">Table of n, a(n) for n = 1..100</a> (terms 1..44 from M. F. Hasler)
%e phi(7) + phi(10) = 6 + 4 = 10; phi(8) + phi(9) = 4 + 6 = 10, so 7 is a term of the sequence.
%t Select[Range[10^5], EulerPhi[ # ] + EulerPhi[ # + 3] == EulerPhi[ # + 1] + EulerPhi[ # + 2] &]
%t Flatten[Position[Partition[EulerPhi[Range[14*10^6]],4,1],_?(#[[1]]+ #[[4]] == #[[2]]+#[[3]]&),{1},Heads->False]] (* _Harvey P. Dale_, Dec 12 2015 *)
%o (PARI) t=vector(4,i,i)~; c=[[1,1,-1,-1],[1,-1,-1,1]]; for(n=1,10^9, t[n%4+1]=eulerphi(n); c[n%2+1]*t & next; print1(n-3,",")) \\ _M. F. Hasler_, Feb 07 2009
%o (Magma) [k: k in [1..10^5] |EulerPhi(k)+EulerPhi(k+3)-EulerPhi(k+1)-EulerPhi(k+2)eq 0]; // _Marius A. Burtea_, Oct 02 2019
%K nonn
%O 1,2
%A _Joseph L. Pe_, Oct 25 2002
%E Terms beyond a(16) from _M. F. Hasler_, Feb 07 2009
|
