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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

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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}]