A297363 Numbers k such that (3^ord(3, k) - 1)/k is prime, where ord(3, k) is the multiplicative order of 3 (mod k).

1, 4, 13, 16, 22, 40, 46, 56, 94, 104, 121, 160, 364, 526, 862, 968, 1093, 1312, 1514, 3146, 3194, 3280, 3742, 4376, 5368, 7280, 7702, 8744, 9841, 28418, 29524, 40880, 69022, 75920, 88573, 106288, 157394

Offset: 1

Author

Amiram Eldar, Dec 29 2017

Keywords

• nonn
• more

Comments

The corresponding primes are 2, 2, 2, 5, 11, 2, 3851, 13, 1001523179, 7, 2, 41, 2, 605199588591144003100881306574406851660288427740394885828171, ...

Examples

			46 is in the sequence since ord(3, 46) = 11 and (3^11 - 1)/46 = 3851 is prime.
		

Crossrefs

Cf. A050975, A053446.

Programs

Mathematica

aQ[n_] := PrimeQ[(3^MultiplicativeOrder[3, n] - 1)/n]; Select[ Range[10000], aQ ]

PARI

isok(n) = (gcd(n,3) == 1) && isprime((3^znorder(Mod(3, n)) - 1)/n); \\ Michel Marcus, Dec 30 2017