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

1,2

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A050975, A053446.

Sequence in context: A165336 A031181 A074262 * A031208 A228137 A301965

Adjacent sequences: A297360 A297361 A297362 * A297364 A297365 A297366

Keyword

nonn,more

Author

Amiram Eldar, Dec 29 2017

Status

approved