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Search: id:A155177
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| A155177 |
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Area ar/6 (divided by 6) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes. |
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+0
7
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| 1, 5, 140, 385, 2870, 8555, 29370, 42925, 93665, 116795, 149226, 155155, 348551, 380380, 414090, 513590, 1229305, 1801800, 2567895, 2767905, 3873301, 3924830, 5053620, 6970150, 17090486, 18362930, 23396450, 31919165, 39336465, 41791750
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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p=1,q=2,a=3,b=4,c=5, ar=3*4/2=6, s=12-+1primes, ...
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MATHEMATICA
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lst={}; Do[p=n; q=p+1; a=q^2-p^2; c=q^2+p^2; b=2*p*q; s=a+b+c; ar=a*b/2; If[PrimeQ[s-1]&&PrimeQ[s+1], AppendTo[lst, ar/6]], {n, 8!}]; lst
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CROSSREFS
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Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176
Sequence in context: A103235 A061463 A091058 this_sequence A054323 A061320 A136464
Adjacent sequences: A155174 A155175 A155176 this_sequence A155178 A155179 A155180
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009
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