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Search: id:A165236
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| A165236 |
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Sorted short legs with no repeats for which there exist at least one Prime Primitive Pythagorean Triples (PPPT) such that all 3 numbers are primes of the form 2*x+1 for x = a, b and c. |
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6
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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; listen)
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OFFSET
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1,1
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COMMENT
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20.21.29, 33.56.65, 44.483.485, 56.783.785, 68.285.293, 273.4136.4145, 303.5096.5105,.. 2*20+1=41 prime, 2*21+1=43 prime, 2*29+1=59 prime, ...
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MATHEMATICA
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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
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Cf. A009004, A020882, A020883, A165158, A165159, A165160
Sequence in context: A134989 A119873 A075230 this_sequence A067468 A127906 A108667
Adjacent sequences: A165233 A165234 A165235 this_sequence A165237 A165238 A165239
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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 09 2009
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