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Search: id:A139924
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| A139924 |
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Primes of the form 8x^2+8xy+41y^2. |
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+0
2
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| 41, 89, 137, 281, 353, 401, 449, 593, 617, 761, 929, 977, 1097, 1217, 1289, 1409, 1553, 1601, 1697, 1721, 1913, 2153, 2273, 2633, 2657, 2777, 2801, 2897, 2969, 3089, 3209, 3257, 3593, 3833, 3881, 4049, 4217, 4337, 4409, 4457, 4649, 4673
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Discriminant=-1248. See A139827 for more information.
Also primes of the forms 32x^2+16xy+41y^2 and 20x^2+12xy+33y^2. See A140633. - T. D. Noe (noe(AT)sspectra.com), May 19 2008
In base 12, the sequence is 35, 75, E5, 1E5, 255, 295, 315, 415, 435, 535, 655, 695, 775, 855, 8E5, 995, X95, E15, E95, EE5, 1135, 12E5, 1395, 1635, 1655, 1735, 1755, 1815, 1875, 1955, 1X35, 1X75, 20E5, 2275, 22E5, 2415, 2535, 2615, 2675, 26E5, 2835, 2855. Moreover, the discriminant is 880 and all primes are {35, 75, E5, 115, 1E5, 215} mod 220. 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
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FORMULA
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The primes are congruent to {41, 89, 137, 161, 281, 305} (mod 312).
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MATHEMATICA
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QuadPrimes[8, -8, 41, 10000] (* see A106856 *)
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CROSSREFS
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Sequence in context: A071886 A087939 A142411 this_sequence A155572 A107145 A087857
Adjacent sequences: A139921 A139922 A139923 this_sequence A139925 A139926 A139927
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 02 2008
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