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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 * A130912 A178844 A210714

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 September 25 21:33 EDT 2017. Contains 292500 sequences.