A002366 Numbers x such that x^2 + y^2 = p^2 = A002144(n)^2, x < y. (Formerly M2442 N0970)

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

1,1

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.

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^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
.................................

Crossrefs

Cf. A002313, A002330, A002331, A376428.

Sequence in context: A240154 A376785 A112656 * A377254 A141615 A075192

Adjacent sequences: A002363 A002364 A002365 * A002367 A002368 A002369

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved