A376338 Numbers k such that phi(k)/2 - 1 = phi(k + 1) where phi = A000010.

11, 19, 43, 49, 67, 163, 211, 283, 331, 523, 547, 691, 787, 907, 1051, 1123, 1171, 1531, 1723, 1867, 2011, 2083, 2251, 2347, 2371, 2467, 2707, 2731, 2803, 2971, 3187, 3307, 3547, 3643, 3907, 3931, 4051, 4243, 4363, 4603, 4651, 4723, 5107, 5227, 5443, 5923

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 20 2024

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000010, A162857, A376337.

Programs

Magma

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

Mathematica

Select[Range[6000], EulerPhi[#]/2-1==EulerPhi[#+1] &] (* Stefano Spezia, Sep 22 2024 *)