A002515 Lucasian primes: p == 3 (mod 4) with 2*p+1 prime. (Formerly M2884 N2039)

3, 11, 23, 83, 131, 179, 191, 239, 251, 359, 419, 431, 443, 491, 659, 683, 719, 743, 911, 1019, 1031, 1103, 1223, 1439, 1451, 1499, 1511, 1559, 1583, 1811, 1931, 2003, 2039, 2063, 2339, 2351, 2399, 2459, 2543, 2699, 2819, 2903, 2939, 2963, 3023, 3299

Offset

1,1

Comments

2*p+1 divides A000225(p), the p-th Mersenne number. - Lekraj Beedassy, Jun 23 2003

Also primes p such that 2^(2*p+1) - 1 divides 2^(2^p-1) - 1. - Arkadiusz Wesolowski, May 26 2011

Intersection of A005384 (Sophie Germain primes) and A002145. - Jeppe Stig Nielsen, Aug 03 2020

References

A. J. C. Cunningham, On Mersenne's numbers, Reports of the British Association for the Advancement of Science, 1894, pp. 563-564.

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.

Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, page 28.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Marius A. Burtea, Table of n, a(n) for n = 1..10000 (terms n = 1..1000 from T. D. Noe)

Mathematica

Select[Range[10^4], Mod[ #, 4] == 3 && PrimeQ[ # ] && PrimeQ[2# + 1] & ]
Select[Prime[Range[500]], Mod[#, 4]==3&&PrimeQ[2#+1]&] (* Harvey P. Dale, Mar 15 2016 *)

Prog

(PARI) is(n)=n%4>2 && isprime(n) && isprime(2*n+1) \\ Charles R Greathouse IV, Apr 01 2013
(Magma) [p: p in PrimesUpTo(6000) | IsPrime(2*p+1) and p mod 4 in [3]]; // Vincenzo Librandi, Sep 03 2016
(MATLAB) p=primes(1500); m=1;
for u=1:length(p)
   if and(isprime(2*p(u)+1)==1, mod(p(u), 4)==3) ; sol(m)=p(u); m=m+1;  end;
end
sol % Marius A. Burtea, Mar 26 2019

Crossrefs

Cf. A002145, A005384.

Sequence in context: A032026 A282198 A158034 * A096297 A081857 A168163

Adjacent sequences: A002512 A002513 A002514 * A002516 A002517 A002518

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Robert G. Wilson v, Mar 07 2002

Status

approved