A091531 Primes p such that k = 2p is the smallest positive solution to the equation phi(p+k) = phi(p) + phi(k), where phi is Euler's totient function.

7, 23, 31, 43, 59, 67, 71, 73, 101, 103, 107, 127, 131, 137, 139, 179, 199, 211, 223, 227, 239, 269, 281, 283, 307, 311, 331, 347, 359, 367, 379, 383, 431, 439, 463, 467, 479, 487, 491, 503, 523, 547, 563, 571, 607, 619, 631, 643, 659, 661, 683, 691, 719, 727

Offset: 1

Author

T. D. Noe, Jan 19 2004

Keywords

• nonn

Comments

Note that for all primes p > 3, phi(3p) = phi(p) + phi(2p).

Crossrefs

Cf. A066426 (least k such that phi(n+k)=phi(n)+phi(k)).

Programs

Mathematica

lst={}; Do[p=Prime[n]; k=1; While[EulerPhi[p+k]!=EulerPhi[p]+EulerPhi[k], k++ ]; If[k==2p, AppendTo[lst, p]], {n, 3, 200}]; lst