A244111 Primes p such that p + phi(p) + mu(phi(p)) is also prime.

19, 37, 97, 157, 199, 229, 271, 307, 337, 379, 577, 601, 661, 727, 811, 829, 877, 937, 997, 1009, 1069, 1171, 1237, 1279, 1297, 1429, 1459, 1531, 1609, 1657, 2029, 2089, 2137, 2179, 2221, 2281, 2467, 2539, 2551, 2557, 2617, 2719, 2791, 2851, 3037, 3061, 3109

Offset

1,1

Comments

For these terms, mu(phi(p)) must be zero.

For prime p, phi(p) = p-1, so terms are primes p such that 2p-1 is also prime (A005382) and p-1 is not squarefree. - Jens Kruse Andersen, Jul 19 2014

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

a(1)=19 as 19+18+0 is prime.
a(2)=37 as 37+36+0 is prime.
a(3)=97 as 97+96+0 is prime.

Maple

with(numtheory): A244111:=n->`if`(isprime(n+phi(n)+mobius(phi(n))) and isprime(n), n, NULL); seq(A244111(n), n=1..5000); # Wesley Ivan Hurt, Jul 19 2014

Mathematica

apQ[n_]:=Module[{p=EulerPhi[n]}, PrimeQ[n+p+MoebiusMu[p]]]; Select[Prime[ Range[500]], apQ] (* Harvey P. Dale, Jun 13 2015 *)

Prog

(PARI) isok(n) = isprime(n) && isprime(n + eulerphi(n) + moebius(eulerphi(n))); \\ Michel Marcus, Jun 21 2014

Crossrefs

Cf. A000010, A005382, A008683.

Sequence in context: A357935 A299930 A053685 * A136063 A242979 A244931

Adjacent sequences: A244108 A244109 A244110 * A244112 A244113 A244114

Keyword

nonn

Author

Torlach Rush, Jun 20 2014

Extensions

More terms from Michel Marcus, Jun 21 2014

Status

approved