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Search: id:A014752
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| A014752 |
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Primes of the form x^2 + 27y^2. |
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12
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| 31, 43, 109, 127, 157, 223, 229, 277, 283, 307, 397, 433, 439, 457, 499, 601, 643, 691, 727, 733, 739, 811, 919, 997, 1021, 1051, 1069, 1093, 1327, 1399, 1423, 1459, 1471, 1579, 1597, 1627, 1657, 1699, 1723, 1753, 1777, 1789, 1801, 1831, 1933, 1999, 2017
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OFFSET
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1,1
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COMMENT
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Primes p such that x^3 = 2 has more than one solution mod p.
Primes p == 1 mod 3 such that p is a cubic residue mod p.
Primes p == 1 mod 6 such that 2 and -2 are both cubes (one implies other) mod p. - Warren Smith (wds(AT)research.nj.nec.com)
Subsequence of A040028, complement of A045309 relative to A040028. Solutions mod p are represented by integers from 0 to p-1. For the terms of this sequence, x^3 = 2 has three solutions mod p, whose sum is p (A059899) or 2*p (A059914). The solutions are given in A060122, A060123 and A060124. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 02 2001
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REFERENCES
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K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1982, Prop. 9.6.2, p. 119.
Bram van Asch, On the structure of the ring Z[2^(1/3)], Internat. J. Pure Appl. Math., 16 (No. 2, 2004), 243-251. See Prop. 7.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).
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MATHEMATICA
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QuadPrimes[1, 0, 27, 10000] (* see A106856 *)
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CROSSREFS
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Cf. A040028, A045309, A059899, A059914, A060122, A060123, A060124.
Sequence in context: A161615 A016108 A059898 this_sequence A020348 A033905 A033661
Adjacent sequences: A014749 A014750 A014751 this_sequence A014753 A014754 A014755
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 02 2001
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EXTENSIONS
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Definition provided by T. D. Noe (noe(AT)sspectra.com), May 08 2005
Entry revised by Michael Somos and N. J. A. Sloane (njas(AT)research.att.com), Jul 28 2006
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