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A216838
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Odd primes for which 2 is not a primitive root.
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12
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7, 17, 23, 31, 41, 43, 47, 71, 73, 79, 89, 97, 103, 109, 113, 127, 137, 151, 157, 167, 191, 193, 199, 223, 229, 233, 239, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 331, 337, 353, 359, 367, 383, 397, 401, 409, 431, 433, 439, 449, 457, 463, 479
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OFFSET
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1,1
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COMMENTS
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Alternately, for these primes p, the polynomial (x^p+1)/(x+1) is reducible over GF(2).
The prime p belongs to this sequence if and only if A002326((p-1)/2) != (p-1). If A002326((p-1)/2) = (p-1), then the prime p belongs to the sequence A001122. - V. Raman, Dec 01 2012
The only primitive root modulo 2 is 1. See A060749. Hence 2 should be added to this sequence in order to obtain the complement of A001122. - Wolfdieter Lang, May 19 2014
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LINKS
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MAPLE
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select(t -> isprime(t) and numtheory[order](2, t) <> t-1, [seq](2*i+1, i=1..1000)); # Robert Israel, May 20 2014
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MATHEMATICA
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Select[Prime[Range[2, 100]], PrimitiveRoot[#] =!= 2 &] (* T. D. Noe, Sep 19 2012 *)
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PROG
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(PARI) forprime(p=3, 1000, if(znorder(Mod(2, p))!=p-1, print(p)))
(PARI) forprime(p=3, 1000, if(factormod((x^p+1)/(x+1), 2, 1)[1, 1]!=(p-1), print(p)))
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CROSSREFS
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Cf. A002326 (multiplicative order of 2 mod 2n+1)
Cf. A001122 (Primes for which 2 is a primitive root)
Cf. A115586 (Primes for which 2 is neither a primitive root nor a quadratic residue).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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