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%I M2884 N2039 #56 Jul 25 2024 10:57:38
%S 3,11,23,83,131,179,191,239,251,359,419,431,443,491,659,683,719,743,
%T 911,1019,1031,1103,1223,1439,1451,1499,1511,1559,1583,1811,1931,2003,
%U 2039,2063,2339,2351,2399,2459,2543,2699,2819,2903,2939,2963,3023,3299
%N Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
%C 2*p+1 divides A000225(p), the p-th Mersenne number. - _Lekraj Beedassy_, Jun 23 2003
%C Also primes p such that 2^(2*p+1) - 1 divides 2^(2^p-1) - 1. - _Arkadiusz Wesolowski_, May 26 2011
%C Intersection of A005384 (Sophie Germain primes) and A002145. - _Jeppe Stig Nielsen_, Aug 03 2020
%D A. J. C. Cunningham, On Mersenne's numbers, Reports of the British Association for the Advancement of Science, 1894, pp. 563-564.
%D L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 27.
%D Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, page 28.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Marius A. Burtea, <a href="/A002515/b002515.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..1000 from T. D. Noe)
%F a(n) >> n log^2 n. - _Charles R Greathouse IV_, Jul 25 2024
%t Select[Range[10^4], Mod[ #, 4] == 3 && PrimeQ[ # ] && PrimeQ[2# + 1] & ]
%t Select[Prime[Range[500]],Mod[#,4]==3&&PrimeQ[2#+1]&] (* _Harvey P. Dale_, Mar 15 2016 *)
%o (PARI) is(n)=n%4>2 && isprime(n) && isprime(2*n+1) \\ _Charles R Greathouse IV_, Apr 01 2013
%o (PARI) list(lim)=my(v=List()); forprimestep(p=3,lim\1,4, if(isprime(2*p+1), listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Jul 25 2024
%o (Magma) [p: p in PrimesUpTo(6000) | IsPrime(2*p+1) and p mod 4 in [3]]; // _Vincenzo Librandi_, Sep 03 2016
%o (MATLAB) p=primes(1500); m=1;
%o for u=1:length(p)
%o if and(isprime(2*p(u)+1)==1, mod(p(u),4)==3) ; sol(m)=p(u); m=m+1; end;
%o end
%o sol % _Marius A. Burtea_, Mar 26 2019
%Y Intersection of A002145 and A005384.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Robert G. Wilson v_, Mar 07 2002