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A002365 Numbers y such that p^2 = x^2 + y^2, 0 < x < y, p = A002144(n).
(Formerly M3430 N1391)
14

%I M3430 N1391

%S 4,12,15,21,35,40,45,60,55,80,72,99,91,112,105,140,132,165,180,168,

%T 195,221,208,209,255,260,252,231,285,312,308,288,299,272,275,340,325,

%U 399,391,420,408,351,425,380,459,440,420,532,520,575,465,551,612,608,609

%N Numbers y such that p^2 = x^2 + y^2, 0 < x < y, p = A002144(n).

%D A. J. C. Cunningham, Quadratic and Linear Tables. Hodgson, London, 1927, pp. 77-79.

%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 60.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002365/b002365.txt">Table of n, a(n) for n = 1..1000</a>

%H A. J. C. Cunningham, <a href="/A002365/a002365.pdf">Quadratic and Linear Tables</a>, Hodgson, London, 1927 [Annotated scanned copy of selected pages]

%e The following table shows the relationship

%e between several closely related sequences:

%e Here p = A002144 = primes == 1 mod 4, p = a^2+b^2 with a < b;

%e a = A002331, b = A002330, t_1 = ab/2 = A070151;

%e p^2 = c^2+d^2 with c < d; c = A002366, d = A002365,

%e t_2 = 2ab = A145046, t_3 = b^2-a^2 = A070079,

%e with {c,d} = {t_2, t_3}, t_4 = cd/2 = ab(b^2-a^2).

%e ---------------------------------

%e .p..a..b..t_1..c...d.t_2.t_3..t_4

%e ---------------------------------

%e .5..1..2...1...3...4...4...3....6

%e 13..2..3...3...5..12..12...5...30

%e 17..1..4...2...8..15...8..15...60

%e 29..2..5...5..20..21..20..21..210

%e 37..1..6...3..12..35..12..35..210

%e 41..4..5..10...9..40..40...9..180

%e 53..2..7...7..28..45..28..45..630

%e .................................

%e 3^2 + 4^2 = 5^2, giving x=3, y=4, p=5 and we have the first terms of A002366, the present sequence and A002144.

%Y Cf. A002144, A002366.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Ray Chandler_, Jun 23 2004

%E Revised definition from _M. F. Hasler_, Feb 24 2009

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Last modified July 8 18:44 EDT 2020. Contains 335524 sequences. (Running on oeis4.)