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

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

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

Crossrefs

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

Sequence in context: A095087 A144517 A225185 * A036259 A004628 A089199

Adjacent sequences: A091528 A091529 A091530 * A091532 A091533 A091534

Keyword

nonn

Author

T. D. Noe, Jan 19 2004

Status

approved