%I #18 Aug 21 2019 06:02:05

%S 3,5,11,23,179,239,359,719,5039,55439,665279,6486479,32432399,

%T 698377679,735134399,1102701599,20951330399,3212537327999,

%U 149602080797769599,299204161595539199,2718551763981393634806325317503999

%N Primes p such that 2*p + 1 is also prime and p + 1 is a highly composite number (definition 1).

%C An equivalent definition of this sequence: odd Sophie Germain primes that differ from a highly composite number by 1.

%C Intersection of A005384 (Sophie Germain primes) and A072828.

%C With the exception of 5, a subsequence of A002515 (Lucasian primes).

%C Except for first two terms, this is a subsequence of A054723.

%C Except for n = 2, 2*a(n) + 1 is a prime factor of A000225(a(n)) (i.e., 2*23 + 1 divides 2^23 - 1).

%C Conjecture: for n >= 5, GCD(A000032(a(n)), A000225(a(n))) = 2*a(n) + 1.

%H Amiram Eldar, <a href="/A214873/b214873.txt">Table of n, a(n) for n = 1..25</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophie_Germain_prime">Sophie Germain prime</a>

%e 23 is a term because both 23 and 47 are primes and also 24 is a highly composite number.

%t lst = {}; a = 0; Do[b = DivisorSigma[0, n + 1]; If[b > a, a = b; If[PrimeQ[n] && PrimeQ[2*n + 1], AppendTo[lst, n]]], {n, 1, 10^6, 2}]; lst

%Y Cf. A054723.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Jul 30 2012