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A014662
Primes p such that order of 2 mod p (=A007733(p)) is even.
7
3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 83, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419
OFFSET
1,1
COMMENTS
Apart from the first term, identical to A091317. - Charles R Greathouse IV, Feb 13 2009
Dirichlet density is 5/24 (Fein, Gordon, & Smith); they show a result on expressing -1 as the sum of two squares relating to this sequence. - Charles R Greathouse IV, May 15 2024
REFERENCES
P. Moree, Appendix to V. Pless et al., Cyclic Self-Dual Z_4 Codes, Finite Fields Applic., vol. 3 pp. 48-69, 1997.
LINKS
Burton Fein, Basil Gordon, and John H. Smith, On the representation of -1 as a sum of two squares in an algebraic number field J. Num. Theor. (1971) Vol. 3, Issue 3, 310-315.
MAPLE
select(t -> isprime(t) and numtheory:-order(2, t)::even, [2*i+1 $ i=1..1000]); # Robert Israel, Aug 12 2014
MATHEMATICA
Select[Prime[Range[80]], EvenQ[MultiplicativeOrder[2, #/(2^IntegerExponent[ #, 2])]]&] (* Jean-François Alcover, Sep 02 2018 *)
PROG
(Magma) [ p: p in PrimesInInterval(3, 419) | IsEven(Modorder(2, p)) ] // Klaus Brockhaus, Dec 09 2008
(PARI) isok(p) = isprime(p) && !(znorder(Mod(2, p/2^valuation(p, 2))) % 2); \\ Michel Marcus, Sep 02 2018
(PARI) is(n)=n>2 && Mod(2, n)^(n>>valuation(n-1, 2))!=1 && isprime(n) \\ Charles R Greathouse IV, May 07 2024
CROSSREFS
The prime terms of A296243.
Cf. A091317.
Sequence in context: A059315 A045403 A059641 * A059349 A045316 A040100
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Klaus Brockhaus, Dec 09 2008
STATUS
approved