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

%I #25 Dec 09 2022 07:07:31

%S 193,3529,9337,27229,46793,78181,90193,112993,135013,437183,849403,

%T 935219,1078579,1283599,1986973,2209583,2341183,2411173,2689693,

%U 2744143,3619069,3712543,4738183,5132983,6596119,7829029,8184713

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

%C For k less than 4*10^6, k is prime, semiprime, or triprime (3-almost prime).

%H 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 a(n) = A066232(n)-2. - _Donovan Johnson_, Oct 14 2011

%e 112993 is in the sequence, because phi(112993) = 106704, phi(112994) = 48384, phi(112995) = 58320 and 106704 = 48384 + 58320.

%p for k from 0 do

%p if numtheory[phi](k) = numtheory[phi](k+1)+numtheory[phi](k+2) then

%p printf("%d\n",k) ;

%p end if;

%p end do: # _R. J. Mathar_, Oct 13 2011

%t Select[Range[10^5], EulerPhi[#] == EulerPhi[# + 1] + EulerPhi[# + 2] &] (* _Alonso del Arte_, Oct 13 2011 *)

%t Position[Partition[EulerPhi[Range[82*10^5]],3,1],_?(#[[1]]==#[[2]]+#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, May 10 2022 *)

%o (PARI) isok(n) = eulerphi(n) == eulerphi(n+1) + eulerphi(n+2); \\ _Michel Marcus_, May 15 2016

%Y Cf. A000010, A066232, A092404.

%K nonn

%O 1,1

%A _Antonio Roldán_, Oct 10 2011

%E a(27) from _Vincenzo Librandi_, Sep 27 2013

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)