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A221982 Primes p == 2 (mod 5) for which 4*p+1 is also prime. 2
7, 37, 67, 97, 127, 277, 307, 487, 577, 727, 997, 1087, 1297, 1327, 1567, 1597, 1777, 1987, 2017, 2437, 2647, 2677, 2767, 2887, 3037, 3067, 3307, 3457, 3637, 3907, 4057, 4297, 4447, 4567, 4987, 5197, 5527, 5557, 6007, 6247, 6337, 6367, 6397, 6547, 6577, 7027, 7057, 7237, 7417, 7507, 7717, 7867 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The corresponding primes 4*p+1 are Chebyshev's subsequence A221981 of the primes with primitive root 10.
REFERENCES
P. L. Chebyshev, Theory of congruences. Elements of number theory, Chelsea, 1972, p. 306.
R. K. Guy, Unsolved Problems in Number Theory, F9.
LINKS
P. Moree, Artin's primitive root conjecture - a survey, arXiv 2004, revised 2012, p. 1.
FORMULA
a(n) = (A221981(n) - 1)/4.
EXAMPLE
7 is a member because 7 == 2 (mod 5) and 29 = 4*7 + 1 are both prime.
MAPLE
A221982:=proc(q)
local n;
for n from 1 to q do
if isprime(n) and isprime(4*n+1) and (n mod 5)=2 then print(n) fi; od; end:
A221982 (10000); # Paolo P. Lava, Feb 12 2013
MATHEMATICA
Select[ Prime[ Range[1000]], Mod[#, 5] == 2 && PrimeQ[4 # + 1] &]
CROSSREFS
Sequence in context: A168003 A132231 A289353 * A104915 A089376 A337423
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 02 2013
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)