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Search: id:A033205
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| A033205 |
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Primes of form x^2+5*y^2. |
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+0
14
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| 5, 29, 41, 61, 89, 101, 109, 149, 181, 229, 241, 269, 281, 349, 389, 401, 409, 421, 449, 461, 509, 521, 541, 569, 601, 641, 661, 701, 709, 761, 769, 809, 821, 829, 881, 929, 941, 1009, 1021, 1049, 1061, 1069
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes congruent to 1,5,9 modulo 20. - Michael Somos Aug 13 2006
Or, 5 and all primes p that divide Fibonacci[(p-1)/2] = A121568[n]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 07 2006
Except for 5, also primes of the form x^2+25y^2. See A140633. - T. D. Noe (noe(AT)sspectra.com), May 19 2008
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REFERENCES
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D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989.
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LINKS
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B. W. Brewer, On primes of the form u^2+5v^2, Am. Math. Monthly vol. 17 no 2 (1966) pp 502-509.
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FORMULA
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A020669 INTERSECT A000040.
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MATHEMATICA
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Clear[f, lst, p, x, y]; f[x_, y_]:=x^2+5*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p]&&p<3542, AppendTo[lst, p]], {y, 0, 2*6!}], {x, 0, 2*6!}]; Take[Union[lst], 5! ] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 04 2009]
QuadPrimes[1, 0, 5, 10000] (* see A106856 *)
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CROSSREFS
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Cf. A121568.
Cf. A139643.
Sequence in context: A115279 A087879 A091729 this_sequence A167742 A107151 A117746
Adjacent sequences: A033202 A033203 A033204 this_sequence A033206 A033207 A033208
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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