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Search: id:A165261
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| A165261 |
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Sorted long 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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+0
2
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| 4, 12, 77, 112, 143, 195, 209, 220, 299, 420, 425, 520, 527, 629, 700, 840, 868, 988, 1023, 1085, 1127, 1209, 1305, 1421, 1480, 1720, 1740, 1900, 2001, 2021, 2255, 2296, 2320, 2331, 2332, 2499, 2520, 2548, 2583, 2604, 2752, 2829, 2964, 3021, 3256, 3311
(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=10^5; 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, b]]]], {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, A165260
Sequence in context: A052558 A133666 A078628 this_sequence A027145 A010370 A081214
Adjacent sequences: A165258 A165259 A165260 this_sequence A165262 A165263 A165264
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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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