# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a214873 Showing 1-1 of 1 %I A214873 #18 Aug 21 2019 06:02:05 %S A214873 3,5,11,23,179,239,359,719,5039,55439,665279,6486479,32432399, %T A214873 698377679,735134399,1102701599,20951330399,3212537327999, %U A214873 149602080797769599,299204161595539199,2718551763981393634806325317503999 %N A214873 Primes p such that 2*p + 1 is also prime and p + 1 is a highly composite number (definition 1). %C A214873 An equivalent definition of this sequence: odd Sophie Germain primes that differ from a highly composite number by 1. %C A214873 Intersection of A005384 (Sophie Germain primes) and A072828. %C A214873 With the exception of 5, a subsequence of A002515 (Lucasian primes). %C A214873 Except for first two terms, this is a subsequence of A054723. %C A214873 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 A214873 Conjecture: for n >= 5, GCD(A000032(a(n)), A000225(a(n))) = 2*a(n) + 1. %H A214873 Amiram Eldar, Table of n, a(n) for n = 1..25 %H A214873 Wikipedia, Sophie Germain prime %e A214873 23 is a term because both 23 and 47 are primes and also 24 is a highly composite number. %t A214873 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 A214873 Cf. A054723. %K A214873 nonn %O A214873 1,1 %A A214873 _Arkadiusz Wesolowski_, Jul 30 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE