Search: id:A070079
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%I A070079
%S A070079 3,5,15,21,35,9,45,11,55,39,65,99,91,15,105,51,85,165,19,95,195,221,105,
%T A070079 209,255,69,115,231,285,25,75,175,299,225,275,189,325,399,391,29,145,
%U A070079 351,425,261,459,279,341,165,231,575,465,551,35,105,609,315,589,385,675
%N A070079 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 y^2 - x^2.
%C A070079 Odd legs of primitive Pythagorean triangles with unique (prime) hypotenuse 
               (A002144), sorted on the latter. Corresponding even legs are given 
               by 4*A070151 (or A145046). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 22 2005
%H A070079 T. D. Noe, <a href="b070079.txt">Table of n, a(n) for n=1..1000</a>
%H A070079 A. F. Labossiere, <a href="http://members.lycos.co.uk/sobalian/hobbies.html">
               Des Triplets Pythagoriciens</a>
%F A070079 a(n)=A079886(n)*A079887(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 13 2003
%e A070079 The following table shows the relationship
%e A070079 between several closely related sequences:
%e A070079 Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;
%e A070079 a = A002331, b = A002330, t_1 = ab/2 = A070151;
%e A070079 p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,
%e A070079 t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,
%e A070079 with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).
%e A070079 ---------------------------------
%e A070079 .p..a..b..t_1..c...d.t_2.t_3..t_4
%e A070079 ---------------------------------
%e A070079 .5..1..2...1...3...4...4...3....6
%e A070079 13..2..3...3...5..12..12...5...30
%e A070079 17..1..4...2...8..15...8..15...60
%e A070079 29..2..5...5..20..21..20..21..210
%e A070079 37..1..6...3..12..35..12..35..210
%e A070079 41..4..5..10...9..40..40...9..180
%e A070079 53..2..7...7..28..45..28..45..630
%e A070079 .................................
%Y A070079 Cf. A002144, A002330, A002331.
%Y A070079 Sequence in context: A063185 A165260 A059528 this_sequence A142717 A057742 
               A101129
%Y A070079 Adjacent sequences: A070076 A070077 A070078 this_sequence A070080 A070081 
               A070082
%K A070079 easy,nonn
%O A070079 1,1
%A A070079 Lekraj Beedassy (blekraj(AT)yahoo.com), May 06 2002
%E A070079 More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 13 2003

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