Search: a105880 -id:a105880
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A167804
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Numbers with primitive root -8.
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+10
19
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5, 23, 25, 29, 47, 53, 71, 101, 125, 149, 167, 173, 191, 197, 239, 263, 269, 293, 311, 317, 359, 383, 389, 461, 479, 503, 509, 529, 557, 599, 625, 647, 653, 677, 701, 719, 743, 773, 797, 821, 839, 841, 863, 887, 941, 983, 1031, 1061, 1109, 1151, 1223, 1229
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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pr=-8; Select[Range[2, 2000], MultiplicativeOrder[pr, # ] == EulerPhi[ # ] &]
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CROSSREFS
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Cf. A105880 (primes with primitive root -8)
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A141171
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Primes of the form -x^2+4*x*y+2*y^2 (as well as of the form 5*x^2+8*x*y+2*y^2).
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+10
8
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2, 5, 23, 29, 47, 53, 71, 101, 149, 167, 173, 191, 197, 239, 263, 269, 293, 311, 317, 359, 383, 389, 431, 461, 479, 503, 509, 557, 599, 647, 653, 677, 701, 719, 743, 773, 797, 821, 839, 863, 887, 911, 941, 983, 1013, 1031, 1061, 1103, 1109, 1151, 1181, 1223, 1229, 1277, 1301, 1319, 1367
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OFFSET
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1,1
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COMMENTS
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Discriminant is 24. Class is 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac and gcd(a, b, c) = 1.
Also primes of form 6*u^2 - v^2. The transformation {u, v} = {y, x - 2*y} yields the form in the title. - Juan Arias-de-Reyna, Mar 19 2011
This is also the list of primes p such that p = 2 or p is congruent to 5 or 23 mod 24 - Jean-François Alcover, Oct 28 2016
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich, Number Theory.
D. B. Zagier, Zetafunktionen und quadratische Körper.
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LINKS
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EXAMPLE
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a(4) = 29 because we can write 29 = -1^2 + 4*1*3 + 2*3^2 (or 29 = 5*1^2 + 8*1*2 + 2*2^2).
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MAPLE
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N:= 10^5: # to get all terms <= N
select(t -> isprime(t) and [isolve(6*u^2-v^2=t)]<>[], [2, seq(op([24*i+5, 24*i+23]), i=0..floor((N-5)/24))]); # Robert Israel, Sep 28 2014
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MATHEMATICA
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CROSSREFS
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For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
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KEYWORD
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nonn
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AUTHOR
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Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008
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STATUS
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approved
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