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A197112 Numbers k such that phi(k) = phi(k+1) + phi(k+2).

%I A197112 #25 Dec 09 2022 07:07:31
%S A197112 193,3529,9337,27229,46793,78181,90193,112993,135013,437183,849403,
%T A197112 935219,1078579,1283599,1986973,2209583,2341183,2411173,2689693,
%U A197112 2744143,3619069,3712543,4738183,5132983,6596119,7829029,8184713
%N A197112 Numbers k such that phi(k) = phi(k+1) + phi(k+2).
%C A197112 For k less than 4*10^6, k is prime, semiprime, or triprime (3-almost prime).
%H A197112 Amiram Eldar, <a href="/A197112/b197112.txt">Table of n, a(n) for n = 1..289</a> (calculated using the b-file at A066232)
%F A197112 a(n) = A066232(n)-2. - _Donovan Johnson_, Oct 14 2011
%e A197112 112993 is in the sequence, because phi(112993) = 106704, phi(112994) = 48384, phi(112995) = 58320  and 106704 = 48384 + 58320.
%p A197112 for k from 0 do
%p A197112         if numtheory[phi](k) = numtheory[phi](k+1)+numtheory[phi](k+2) then
%p A197112                 printf("%d\n",k) ;
%p A197112         end if;
%p A197112 end do: # _R. J. Mathar_, Oct 13 2011
%t A197112 Select[Range[10^5], EulerPhi[#] == EulerPhi[# + 1] + EulerPhi[# + 2] &] (* _Alonso del Arte_, Oct 13 2011 *)
%t A197112 Position[Partition[EulerPhi[Range[82*10^5]],3,1],_?(#[[1]]==#[[2]]+#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, May 10 2022 *)
%o A197112 (PARI) isok(n) = eulerphi(n) == eulerphi(n+1) + eulerphi(n+2); \\ _Michel Marcus_, May 15 2016
%Y A197112 Cf. A000010, A066232, A092404.
%K A197112 nonn
%O A197112 1,1
%A A197112 _Antonio Roldán_, Oct 10 2011
%E A197112 a(27) from _Vincenzo Librandi_, Sep 27 2013