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Search: id:A155175
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| A155175 |
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Hypotenuse C 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, s=a+b+c, s-+1 are primes. |
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+0
9
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| 5, 13, 113, 221, 841, 1741, 3961, 5101, 8581, 9941, 11705, 12013, 20605, 21841, 23113, 26681, 47741, 61601, 78013, 82013, 102605, 103513, 122513, 151801, 276025, 289561, 340313, 418613, 481181, 501001, 660101, 711625, 838513, 901825, 931613
(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,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; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], 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
Sequence in context: A117437 A106046 A117527 this_sequence A004063 A005764 A099974
Adjacent sequences: A155172 A155173 A155174 this_sequence A155176 A155177 A155178
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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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