cp's OEIS Frontend

A002515 Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.

%I A002515 M2884 N2039 #59 Apr 03 2025 14:59:50
%S A002515 3,11,23,83,131,179,191,239,251,359,419,431,443,491,659,683,719,743,
%T A002515 911,1019,1031,1103,1223,1439,1451,1499,1511,1559,1583,1811,1931,2003,
%U A002515 2039,2063,2339,2351,2399,2459,2543,2699,2819,2903,2939,2963,3023,3299
%N A002515 Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
%C A002515 2*p+1 divides A000225(p), the p-th Mersenne number. - _Lekraj Beedassy_, Jun 23 2003
%C A002515 Also primes p such that 2^(2*p+1) - 1 divides 2^(2^p-1) - 1. - _Arkadiusz Wesolowski_, May 26 2011
%C A002515 Intersection of A005384 (Sophie Germain primes) and A002145. - _Jeppe Stig Nielsen_, Aug 03 2020
%D A002515 A. J. C. Cunningham, On Mersenne's numbers, Reports of the British Association for the Advancement of Science, 1894, pp. 563-564.
%D A002515 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 A002515 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 76.
%D A002515 Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, page 28.
%D A002515 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002515 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002515 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 A002515 a(n) >> n log^2 n. - _Charles R Greathouse IV_, Jul 25 2024
%t A002515 Select[Range[10^4], Mod[ #, 4] == 3 && PrimeQ[ # ] && PrimeQ[2# + 1] & ]
%t A002515 Select[Prime[Range[500]],Mod[#,4]==3&&PrimeQ[2#+1]&] (* _Harvey P. Dale_, Mar 15 2016 *)
%o A002515 (PARI) is(n)=n%4>2 && isprime(n) && isprime(2*n+1) \\ _Charles R Greathouse IV_, Apr 01 2013
%o A002515 (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 A002515 (Magma) [p: p in PrimesUpTo(6000) | IsPrime(2*p+1) and p mod 4 in [3]]; // _Vincenzo Librandi_, Sep 03 2016
%o A002515 (MATLAB) p=primes(1500); m=1;
%o A002515 for u=1:length(p)
%o A002515    if and(isprime(2*p(u)+1)==1, mod(p(u),4)==3) ; sol(m)=p(u); m=m+1;  end;
%o A002515 end
%o A002515 sol % _Marius A. Burtea_, Mar 26 2019
%Y A002515 Intersection of A002145 and A005384.
%K A002515 nonn,easy
%O A002515 1,1
%A A002515 _N. J. A. Sloane_
%E A002515 More terms from _Robert G. Wilson v_, Mar 07 2002