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
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)
FORMULA
a(n) >> n log^2 n. - Charles R Greathouse IV, Jul 25 2024
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
(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
sol % Marius A. Burtea, Mar 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Mar 07 2002
STATUS
approved