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 A156681 Consider all Pythagorean triangles A^2 + B^2 = C^2 with A < B < C; sequence gives values of B, sorted to correspond to increasing A (A009004). 6
 4, 12, 8, 24, 15, 12, 40, 24, 60, 16, 35, 84, 48, 20, 36, 112, 30, 63, 144, 24, 80, 180, 21, 48, 99, 28, 72, 220, 120, 264, 32, 45, 70, 143, 60, 312, 168, 36, 120, 364, 45, 96, 195, 420, 40, 72, 224, 480, 60, 126, 255, 44, 56, 180, 544, 288, 84, 120, 612, 48, 77, 105 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The ordered sequence of B values is A009012(n) (allowing repetitions) and A009023(n) (excluding repetitions). REFERENCES Albert H. Beiler, Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134. W. Sierpinski, Pythagorean Triangles, Dover Publications, Inc., Mineola, New York, 2003. LINKS Shujing Lyu, Table of n, a(n) for n = 1..5000 Robert Recorde, The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers, London, 1557. See p. 57. FORMULA a(n) = sqrt(A156682(n)^2 - A009004(n)^2). EXAMPLE As the first four Pythagorean triples (ordered by increasing A) are (3,4,5), (5,12,13), (6,8,10) and (7,24,25), then a(1)=4, a(2)=12, a(3)=8 and a(4)=24. MATHEMATICA PythagoreanTriplets[n_]:=Module[{t={{3, 4, 5}}, i=4, j=5}, While[i

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Last modified August 14 23:38 EDT 2022. Contains 356122 sequences. (Running on oeis4.)