A002366 Numbers x such that x^2 + y^2 = p^2 = A002144(n)^2, x < y.
3, 5, 8, 20, 12, 9, 28, 11, 48, 39, 65, 20, 60, 15, 88, 51, 85, 52, 19, 95, 28, 60, 105, 120, 32, 69, 115, 160, 68, 25, 75, 175, 180, 225, 252, 189, 228, 40, 120, 29, 145, 280, 168, 261, 220, 279, 341, 165, 231, 48, 368, 240, 35, 105, 200, 315, 300, 385, 52, 260, 259
Offset: 1
Keywords
Examples
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
.................................
References
- A. J. C. Cunningham, Quadratic and Linear Tables. Hodgson, London, 1927, pp. 77-79.
- D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 60.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Hugo Pfoertner, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
- A. J. C. Cunningham, Quadratic and Linear Tables, Hodgson, London, 1927 [Annotated scanned copy of selected pages]
- Hugo Pfoertner, Plot of log(a(n)) vs log(A002144(n)) using Plot 2.
Extensions
More terms from Ray Chandler, Jun 23 2004
Corrected definition to require p=A002144(n), which defines the order of the terms. - M. F. Hasler, Feb 24 2009