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Search: id:A155187
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| A155187 |
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Prime numbers q of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, p+1=q(prime), 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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1
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| 2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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p=1,q=2(prime),a=3,b=4,c=5,s=12-+1 primes, ...
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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; ar=a*b/2; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], If[PrimeQ[q], AppendTo[lst, q]]], {n, 8!}]; lst
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CROSSREFS
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Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281
Sequence in context: A066046 A065597 A001052 this_sequence A109132 A008510 A042165
Adjacent sequences: A155184 A155185 A155186 this_sequence A155188 A155189 A155190
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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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