A265850 - OEIS

%I #37 Jul 27 2024 02:54:24

%S 5,11,17,160,257,65537

%N Numbers n such that phi(n-2) = phi(n+5) - 2.

%C Also numbers n such that cototient(n-2) = cototient(n+5) - 5, where cototient(x) = A051953(x).

%C The next term, if it exists, must be greater than 2*10^7.

%C The first 4 known Fermat primes > 3 from A019434 are in the sequence.

%C Prime terms are in the sequence A265851.

%C The next term if it exists is greater than 10^9. - _Michel Marcus_, Dec 20 2015

%C The next term if it exists is greater than 10^11. - _Dana Jacobsen_, Dec 24 2015

%e 160 is in the sequence because phi(158) = phi(165) - 2 = 78.

%t aa={}; Do[If[EulerPhi[n - 2] == EulerPhi[n + 5] - 2, AppendTo[aa, n]], {n, 1, 2 10^5}]; aa (* _Vincenzo Librandi_, Dec 17 2015 *)

%t Flatten[Position[Partition[EulerPhi[Range[66000]],8,1],_?(#[[1]]== #[[-1]] -2&),1,Heads->False]]+2 (* _Harvey P. Dale_, Dec 31 2021 *)

%o (Magma) [n: n in [3..100000] | EulerPhi(n-2) eq EulerPhi(n+5)-2];

%o (PARI) for(n=3, 1e4, if(eulerphi(n-2) == eulerphi(n+5) - 2, print1(n, ", "))) \\ _Altug Alkan_, Dec 16 2015

%Y Cf. A000010, A019434, A051953, A265851.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Dec 16 2015