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A165236
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Short legs of primitive Pythagorean Triples (a,b,c) such that 2*a+1, 2*b+1 and 2*c+1 are primes.
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3
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20, 33, 44, 56, 68, 273, 303, 320, 380, 440, 483, 740, 1071, 1089, 1101, 1220, 1376, 1484, 1635, 1773, 1808, 1869, 1940, 1965, 2000, 2120, 2144, 2204, 2319, 2715, 2763, 3003, 3164, 3309, 3500, 3603, 3729, 3740, 3753, 3801, 4148, 4215, 4323, 4340, 4401
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Only one instance of a enters the sequence if multiple solutions exist, like with (a,b,c) = (320,999,1049) and (a,b,c) = (320,25599,25601).
Subsequence of A009004. [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 25 2010]
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EXAMPLE
| (a,b,c) = (20,21,29), (33,56,65), (44,483,485), (56,783,785), (68,285,293), (273,4136,4145).
In the first case, for example, 2*20+1=41, 2*21+1 and 2*29+1 are all prime, which adds the half-leg 20 to the sequence.
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MATHEMATICA
| amax=6*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; If[PrimeQ[2*a+1], b=2*m*n; If[PrimeQ[2*b+1], If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]];
c=m^2+n^2; If[PrimeQ[2*c+1], k++; AppendTo[lst, a]]]]]]; If[a>amax, Break[]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst
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CROSSREFS
| Cf. A009004, A020883, A165237, A165238
Sequence in context: A134989 A119873 A075230 * A067468 A127906 A108667
Adjacent sequences: A165233 A165234 A165235 * A165237 A165238 A165239
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 09 2009
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EXTENSIONS
| Comments moved to examples and definition clarified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 25 2010
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