A376338 - OEIS

%I #7 Oct 18 2024 18:13:53

%S 11,19,43,49,67,163,211,283,331,523,547,691,787,907,1051,1123,1171,

%T 1531,1723,1867,2011,2083,2251,2347,2371,2467,2707,2731,2803,2971,

%U 3187,3307,3547,3643,3907,3931,4051,4243,4363,4603,4651,4723,5107,5227,5443,5923

%N Numbers k such that phi(k)/2 - 1 = phi(k + 1) where phi = A000010.

%C Conjecture: this sequence is the union {49} and the primes of the form 4*p - 1 where p odd prime.

%e Number 49 is in this sequence because phi(49)/2 - 1 = 42/2 - 1 = 21 - 1 = 20 is equal to phi(49 + 1) = phi(50) = 20.

%t Select[Range[6000], EulerPhi[#]/2-1==EulerPhi[#+1] &] (* _Stefano Spezia_, Sep 22 2024 *)

%o (Magma) [k: k in [3..6000] | ((EulerPhi(k) div 2) - 1) eq EulerPhi(k + 1)];

%Y Cf. A000010, A162857, A376337.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Sep 20 2024