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 A070151 a(n) is one fourth of the even leg of the unique primitive Pythagorean triangle with hypotenuse A002144(n). 15
 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, 63, 40, 17, 78, 77, 72, 45, 68, 63, 85, 57, 10, 30, 105, 102, 70, 42, 95, 55, 110, 105, 133, 130, 12, 92, 60, 153, 152, 50, 143, 75, 138, 13, 65, 165, 27, 117, 190, 150, 187, 143, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 FORMULA a(n) = A002330(n+1)*A002331(n+1)/2. - David Wasserman, May 12 2003 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 EXAMPLE The following table shows the relationship between several closely related sequences: Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b; a = A002331, b = A002330, t_1 = ab/2 = A070151; p^2 = c^2+d^2 with c < d; c = A002366, d = A002365, t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079, with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2). --------------------------------- .p..a..b..t_1..c...d.t_2.t_3..t_4 --------------------------------- .5..1..2...1...3...4...4...3....6 13..2..3...3...5..12..12...5...30 17..1..4...2...8..15...8..15...60 29..2..5...5..20..21..20..21..210 37..1..6...3..12..35..12..35..210 41..4..5..10...9..40..40...9..180 53..2..7...7..28..45..28..45..630 ................................. 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 CROSSREFS Cf. A002144, A002330, A002331, A070079, A080109, A144954, A144960. Sequence in context: A281668 A132817 A131025 * A331847 A130912 A178844 Adjacent sequences:  A070148 A070149 A070150 * A070152 A070153 A070154 KEYWORD easy,nonn AUTHOR Lekraj Beedassy, May 06 2002 EXTENSIONS Edited. New name, moved the old one to the comment section. - Wolfdieter Lang, Jan 13 2015 STATUS approved

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Last modified December 5 19:53 EST 2020. Contains 338965 sequences. (Running on oeis4.)