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A002515
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Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
(Formerly M2884 N2039)
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43
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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
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history;
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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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).
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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