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 A221981 Primes q = 4*p+1, where p == 2 (mod 5) is also prime. 4
 29, 149, 269, 389, 509, 1109, 1229, 1949, 2309, 2909, 3989, 4349, 5189, 5309, 6269, 6389, 7109, 7949, 8069, 9749, 10589, 10709, 11069, 11549, 12149, 12269, 13229, 13829, 14549, 15629, 16229, 17189, 17789, 18269, 19949, 20789, 22109, 22229, 24029, 24989, 25349, 25469, 25589, 26189, 26309, 28109, 28229, 28949, 29669, 30029, 30869, 31469, 32069, 33149, 34589, 34949, 36269, 36629, 36749, 37589 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Moree (2012) says that Chebyshev observed that if q = 4p + 1 is prime, with prime p == 2 (mod 5), then 10 is a primitive root modulo q. If the sequence is infinite, then Artin's conjecture ("every nonsquare integer n != -1 is a primitive root of infinitely many primes q") is true for n = 10. The corresponding primes p are A221982. The sequence is infinite under Dickson's conjecture, thus Dickson's conjecture implies Artin's conjecture for n = 10. - Charles R Greathouse IV, Apr 18 2013 REFERENCES P. L. Chebyshev, Theory of congruences, Elements of number theory, Chelsea, 1972, p. 306. Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section F9, pp. 377-380. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 P. L. Chebyshev, Theorie der Congruenzen, Mayer & Mueller, 1889, pp. 306-313. Pieter Moree, Artin's primitive root conjecture - a survey, arXiv:math/0412262 [math.NT], 2004, revised 2012, p. 1. Index entries for sequences related to Artin's conjecture Index entries for primes by primitive root FORMULA a(n) = 4*A221982(n) + 1. EXAMPLE 29 is a member because 29 = 4*7 + 1 and 7 == 2 (mod 5) are prime. MAPLE A221981:=n->`if`(isprime(4*n+1) and isprime(n) and n mod 5 = 2, 4*n+1, NULL): seq(A221981(n), n=1..10^4); # Wesley Ivan Hurt, Dec 11 2015 MATHEMATICA Select[ Prime[ Range[4000]], Mod[(# - 1)/4, 5] == 2 && PrimeQ[(# - 1)/4] &] PROG (PARI) is(n)=n%20==9 && isprime(n) && isprime(n\4) \\ Charles R Greathouse IV, Apr 18 2013 CROSSREFS Cf. A001913, A005596, A006883, A045380, A106849, A221982, A222008. Sequence in context: A172075 A042644 A263126 * A139997 A103565 A098117 Adjacent sequences: A221978 A221979 A221980 * A221982 A221983 A221984 KEYWORD nonn AUTHOR Jonathan Sondow, Feb 02 2013 STATUS approved

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Last modified April 23 08:11 EDT 2024. Contains 371905 sequences. (Running on oeis4.)