Search: id:A140615
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%I A140615
%S A140615 13,61,109,277,349,373,541,613,733,853,877,997,1069,1117,1381,1429,1597,
%T A140615 1669,1693,1789,1861,1933,2053,2221,2389,2437,2749,2917,3109,3181,3229,
%U A140615 3253,3373,3517,3541,3637,3709,4021,4549,4597,4813,4861
%N A140615 Primes of the form 13x^2+6xy+21y^2.
%C A140615 Discriminant=-1056. Also primes of the form 13x^2+2xy+61y^2.
%C A140615 In base 12, the sequence is 11, 51, 91, 1E1, 251, 271, 391, 431, 511, 
               5E1, 611, 6E1, 751, 791, 971, 9E1, E11, E71, E91, 1051, 10E1, 1151, 
               1231, 1351, 1471, 14E1, 1711, 1831, 1971, 1X11, 1X51, 1X71, 1E51, 
               2051, 2071, 2131, 2191, 23E1, 2771, 27E1, 2951, 2991, where X is 
               10 and E is 11. Moreover, the discriminant is -740. Keep in mind 
               that 12 is a canonical base for mathematics in general since any 
               prime greater than 3 is of the form 6k+-1, any prime of the form 
               4k+1 is a sum of squares while any prime of the form 4k+3 is never 
               a sum of squares and lcm(6,4)=12. - Walter A. Kehowski (wkehowski(AT)cox.net), 
               May 31 2008
%t A140615 Union[QuadPrimes[13, 6, 21, 10000], QuadPrimes[13, -6, 21, 10000]] (* 
               see A106856 *)
%Y A140615 Cf. A140633.
%Y A140615 Sequence in context: A028874 A087106 A142402 this_sequence A086361 A119151 
               A081589
%Y A140615 Adjacent sequences: A140612 A140613 A140614 this_sequence A140616 A140617 
               A140618
%K A140615 nonn,easy
%O A140615 1,1
%A A140615 T. D. Noe (noe(AT)sspectra.com), May 19 2008

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