A188130 - OEIS

%I #18 Aug 27 2021 17:37:46

%S 5,37,73,233,397,461,557,577,601,761,1013,1321,1361,1381,1453,1693,

%T 1777,1993,2417,2593,2621,2897,3037,3181,3457,3581,3593,4001,4273,

%U 4441,4517,4597,4801,4813,4861,4933,5197,5393,5557,5717,5801,6173,6277,6353,6373,6841,6977,7573,7853,7901,8353,8377,9613,10321,10357

%N Primes p such that 6p+1 divides the Mersenne number M(p)=A000225(p).

%C These primes are such that p=1 (mod 4) and 6p+1 is prime, but there are other primes with these properties (13, 17, ...) not in this sequence.

%C There are no primes p such that 4p+1 divides M(p), but those for which 2p+1 divides M(p) are the Lucasian primes A002515, and those for which 10p+1 divides M(p) are listed in A188133.

%H Amiram Eldar, <a href="/A188130/b188130.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1313 from M. F. Hasler)

%t Select[Range[10^4], PrimeQ[#] && PowerMod[2, #, 6# + 1] == 1 &] (* _Amiram Eldar_, Nov 13 2019 *)

%o (PARI) forprime(p=1,1e5,Mod(2,p*6+1)^p-1||print1(p", "))

%Y Cf. A002515, A188133.

%Y Primes in A038844.

%K nonn

%O 1,1

%A _M. F. Hasler_, Mar 21 2011