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Search: id:A155185
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| 5, 13, 841, 1741, 3961, 5101, 8581, 276025, 289561, 711625, 2906461, 3545785, 3723721, 4533061, 5187421, 5284501, 5947801, 11286001, 19052965, 21773401, 23344945, 26129221, 37575781, 41032741, 43459165, 45324721, 47229481
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Hypotenuse C (prime numbers only) 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. p=1,q=2,a=3,b=4,c=5=prime,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; ar=a*b/2; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], If[PrimeQ[a], AppendTo[lst, c]]], {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
Adjacent sequences: A155182 A155183 A155184 this_sequence A155186 A155187 A155188
Sequence in context: A012033 A007540 A157250 this_sequence A009157 A153374 A012032
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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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