cp's OEIS Frontend

A002366 Numbers x such that x^2 + y^2 = p^2 = A002144(n)^2, x < y.

%I A002366 M2442 N0970 #29 Sep 23 2024 08:07:56
%S A002366 3,5,8,20,12,9,28,11,48,39,65,20,60,15,88,51,85,52,19,95,28,60,105,
%T A002366 120,32,69,115,160,68,25,75,175,180,225,252,189,228,40,120,29,145,280,
%U A002366 168,261,220,279,341,165,231,48,368,240,35,105,200,315,300,385,52,260,259
%N A002366 Numbers x such that x^2 + y^2 = p^2 = A002144(n)^2, x < y.
%D A002366 A. J. C. Cunningham, Quadratic and Linear Tables. Hodgson, London, 1927, pp. 77-79.
%D A002366 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 60.
%D A002366 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002366 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002366 Hugo Pfoertner, <a href="/A002366/b002366.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A002366 A. J. C. Cunningham, <a href="/A002365/a002365.pdf">Quadratic and Linear Tables</a>, Hodgson, London, 1927 [Annotated scanned copy of selected pages]
%H A002366 Hugo Pfoertner, <a href="/plot2a?graph=1&amp;name1=A002144&amp;name2=A002366&amp;tform1=log%20base%2010&amp;tform2=log%20base%2010&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Plot of log(a(n)) vs log(A002144(n))</a> using Plot 2.
%e A002366 The following table shows the relationship
%e A002366 between several closely related sequences:
%e A002366 Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;
%e A002366 a = A002331, b = A002330, t_1 = ab/2 = A070151;
%e A002366 p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,
%e A002366 t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,
%e A002366 with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).
%e A002366 ---------------------------------
%e A002366 .p..a..b..t_1..c...d.t_2.t_3..t_4
%e A002366 ---------------------------------
%e A002366 .5..1..2...1...3...4...4...3....6
%e A002366 13..2..3...3...5..12..12...5...30
%e A002366 17..1..4...2...8..15...8..15...60
%e A002366 29..2..5...5..20..21..20..21..210
%e A002366 37..1..6...3..12..35..12..35..210
%e A002366 41..4..5..10...9..40..40...9..180
%e A002366 53..2..7...7..28..45..28..45..630
%e A002366 .................................
%Y A002366 Cf. A002313, A002330, A002331, A376428.
%K A002366 nonn
%O A002366 1,1
%A A002366 _N. J. A. Sloane_
%E A002366 More terms from _Ray Chandler_, Jun 23 2004
%E A002366 Corrected definition to require p=A002144(n), which defines the order of the terms. - _M. F. Hasler_, Feb 24 2009