Search: id:A014752
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%I A014752
%S A014752 31,43,109,127,157,223,229,277,283,307,397,433,439,457,499,601,643,691,
%T A014752 727,733,739,811,919,997,1021,1051,1069,1093,1327,1399,1423,1459,1471,
%U A014752 1579,1597,1627,1657,1699,1723,1753,1777,1789,1801,1831,1933,1999,2017
%N A014752 Primes of the form x^2 + 27y^2.
%C A014752 Primes p such that x^3 = 2 has more than one solution mod p.
%C A014752 Primes p == 1 mod 3 such that p is a cubic residue mod p.
%C A014752 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)
%C A014752 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
%D A014752 K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 
               Springer, 1982, Prop. 9.6.2, p. 119.
%D A014752 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.
%H A014752 T. D. Noe, <a href="b014752.txt">Table of n, a(n) for n = 1..1000</a>
%H A014752 S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of 
               Euler's q-Series</a>, (arXiv:math.NT/0701251).
%t A014752 QuadPrimes[1, 0, 27, 10000] (* see A106856 *)
%Y A014752 Cf. A040028, A045309, A059899, A059914, A060122, A060123, A060124.
%Y A014752 Sequence in context: A161615 A016108 A059898 this_sequence A020348 A033905 
               A033661
%Y A014752 Adjacent sequences: A014749 A014750 A014751 this_sequence A014753 A014754 
               A014755
%K A014752 nonn
%O A014752 1,1
%A A014752 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 02 2001
%E A014752 Definition provided by T. D. Noe (noe(AT)sspectra.com), May 08 2005
%E A014752 Entry revised by Michael Somos and N. J. A. Sloane (njas(AT)research.att.com), 
               Jul 28 2006

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