A237183 Primes p with phi(p+1) - 1 and phi(p+1) + 1 both prime, where phi(.) is Euler's totient function.

7, 11, 13, 17, 37, 41, 53, 61, 97, 151, 181, 197, 227, 233, 251, 269, 277, 397, 433, 457, 487, 541, 557, 571, 593, 619, 631, 719, 743, 769, 839, 857, 929, 941, 947, 953, 1013, 1021, 1049, 1061, 1063, 1201, 1237, 1277, 1307, 1321, 1367, 1481, 1511, 1549

Offset

1,1

Comments

According to part (i) of the conjecture in A237168, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 7 since 7, phi(7+1) - 1 = 3 and phi(7+1) + 1 = 5 are all prime, but phi(2+1) - 1 = phi(3+1) - 1 = phi(5+1) - 1 = 1 is not prime.

Mathematica

PQ[n_]:=PrimeQ[EulerPhi[n]-1]&&PrimeQ[EulerPhi[n]+1]
n=0; Do[If[PQ[Prime[k]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10000}]
Select[Prime[Range[300]], And@@PrimeQ[EulerPhi[#+1]+{1, -1}]&] (* Harvey P. Dale, Mar 06 2014 *)

Prog

(PARI) s=[]; forprime(p=2, 2000, if(isprime(eulerphi(p+1)-1) && isprime(eulerphi(p+1)+1), s=concat(s, p))); s \\ Colin Barker, Feb 04 2014

Crossrefs

Cf. A000010, A000040, A001359, A006512, A072281, A237127, A237130, A237168.

Sequence in context: A038877 A019351 A032666 * A153321 A060772 A257125

Adjacent sequences: A237180 A237181 A237182 * A237184 A237185 A237186

Keyword

nonn

Author

Zhi-Wei Sun, Feb 04 2014

Status

approved