

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
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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^2a^2 = A070079,
with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2a^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



