A297362 - OEIS

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).

%I #14 Aug 26 2023 03:44:07

%S 5,9,21,23,33,47,51,73,85,89,93,129,167,217,223,263,315,341,381,585,

%T 819,1057,1365,3591,3855,4681,4871,5461,6141,6223,6719,7487,8193,

%U 11447,13107,13367,13797,14329,16513,18631,21845,24573,25575,26431,33825,37449

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

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

%H Amiram Eldar, <a href="/A297362/b297362.txt">Table of n, a(n) for n = 1..64</a>

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

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

%o (PARI) is(n) = n%2 && isprime((2^znorder(Mod(2, n))-1)/n); \\ _Amiram Eldar_, Aug 26 2023

%Y Cf. A002326, A165781.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 29 2017