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Search: id:A165260
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| A165260 |
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Sorted short legs with no repeats of Primitive Pythagorean Triples (PPT) if sum of all 3 sides are averages of twin prime pairs. |
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3
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| 3, 5, 15, 21, 24, 28, 36, 41, 59, 64, 89, 100, 101, 120, 131, 132, 141, 153, 155, 168, 180, 203, 204, 208, 209, 215, 220, 231, 244, 280, 288, 300, 309, 315, 336, 341, 348, 351, 395, 405, 408, 429, 448, 453, 455, 495, 520, 540, 551, 567, 568, 580, 592, 636, 648
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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3.4.5, 5.12.13, 15.112.113, 21.220.221, 24.143.145, 28.195.197, 36.77.85, 41.840.841, 59.1740.1741, 64.1023.1025, 89.3960.3961, 100.2499.2501 3+4+5=12 -> 11 and 13 are primes, 5+12+13=30 -> 29 and 31 are primes, ..
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MATHEMATICA
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amax=10^4; lst={}; k=0; q=12!; Do[If[(e=((n+1)^2-n^2))>amax, Break[]]; Do[If[GCD[m, n]==1, a=m^2-n^2; b=2*m*n; If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]]; c=m^2+n^2; x=a+b+c; If[PrimeQ[x-1]&&PrimeQ[x+1], k++; AppendTo[lst, a]]]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst
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CROSSREFS
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Cf. A009004, A020882, A020883, A165158, A165159, A165160, A165236, A165237, A165238
Sequence in context: A018374 A002962 A063185 this_sequence A059528 A070079 A142717
Adjacent sequences: A165257 A165258 A165259 this_sequence A165261 A165262 A165263
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KEYWORD
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nonn,uned
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2009
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