A297362 Numbers k such that (2^ord(2, k) - 1)/k is prime, where ord(2, k) is the multiplicative order of 2 (mod k).

5, 9, 21, 23, 33, 47, 51, 73, 85, 89, 93, 129, 167, 217, 223, 263, 315, 341, 381, 585, 819, 1057, 1365, 3591, 3855, 4681, 4871, 5461, 6141, 6223, 6719, 7487, 8193, 11447, 13107, 13367, 13797, 14329, 16513, 18631, 21845, 24573, 25575, 26431, 33825, 37449

Offset: 1

Author

Amiram Eldar, Dec 29 2017

Keywords

• nonn

Comments

The corresponding primes are 3, 7, 3, 89, 31, 178481, 5, 7, 3, 23, 11, ...

Examples

			5 is in the sequence since ord(2, 5) = 4 and (2^4 - 1)/5 = 3 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A002326, A165781.

Programs

Mathematica

aQ[n_] := PrimeQ[(2^MultiplicativeOrder[2, n] - 1)/n]; Select[Range[10000],aQ]

PARI

is(n) = n%2 && isprime((2^znorder(Mod(2, n))-1)/n); \\ Amiram Eldar, Aug 26 2023