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%I #16 Jan 10 2017 05:00:46
%S 1,3,2,5,3,10,7,15,12,20,18,5,15,28,22,35,33,13,45,42,7,15,52,30,8,65,
%T 63,40,17,78,77,72,45,68,63,85,57,10,30,105,102,70,42,95,55,110,105,
%U 133,130,12,92,60,153,152,50,143,75,138,13,65,165,27,117,190,150,187,143,70
%N a(n) is one fourth of the even leg of the unique primitive Pythagorean triangle with hypotenuse A002144(n).
%C Consider sequence A002144 of primes congruent to 1 (mod 4) and equal to x^2 + y^2, with y>x given by A002330 and A002331; sequence gives values x*y/2.
%H T. D. Noe, <a href="/A070151/b070151.txt">Table of n, a(n) for n=1..1000</a>
%F a(n) = A002330(n+1)*A002331(n+1)/2. - _David Wasserman_, May 12 2003
%F 4*a(n) is the even positive integer with A080109(n) = A002144(n)^2 = A070079(n)^2 + (4*a(n))^2 in this unique decomposition (up to order). See A080109 for references. - _Wolfdieter Lang_, Jan 13 2015
%e The following table shows the relationship
%e between several closely related sequences:
%e Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;
%e a = A002331, b = A002330, t_1 = ab/2 = A070151;
%e p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,
%e t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,
%e with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).
%e ---------------------------------
%e .p..a..b..t_1..c...d.t_2.t_3..t_4
%e ---------------------------------
%e .5..1..2...1...3...4...4...3....6
%e 13..2..3...3...5..12..12...5...30
%e 17..1..4...2...8..15...8..15...60
%e 29..2..5...5..20..21..20..21..210
%e 37..1..6...3..12..35..12..35..210
%e 41..4..5..10...9..40..40...9..180
%e 53..2..7...7..28..45..28..45..630
%e .................................
%e n = 7: a(7) = 7, A002144(7) = 53 and 53^2 = 2809 = A070079(7)^2 + (4*a(7))^2 = 45^2 + (4*7)^2 = 2025 + 784. - _Wolfdieter Lang_, Jan 13 2015
%Y Cf. A002144, A002330, A002331, A070079, A080109, A144954, A144960.
%K easy,nonn
%O 1,2
%A _Lekraj Beedassy_, May 06 2002
%E Edited. New name, moved the old one to the comment section. - _Wolfdieter Lang_, Jan 13 2015
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