A002365 - OEIS

A002365

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

4, 12, 15, 21, 35, 40, 45, 60, 55, 80, 72, 99, 91, 112, 105, 140, 132, 165, 180, 168, 195, 221, 208, 209, 255, 260, 252, 231, 285, 312, 308, 288, 299, 272, 275, 340, 325, 399, 391, 420, 408, 351, 425, 380, 459, 440, 420, 532, 520, 575, 465, 551, 612, 608, 609

(list; graph; refs; listen; history; text; internal format)

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]

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

.................................

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.

CROSSREFS

Cf. A002144, A002366, A376429.

Sequence in context: A024354 A020883 A376429 * A212245 A046087 A081872

Adjacent sequences: A002362 A002363 A002364 * A002366 A002367 A002368

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Ray Chandler, Jun 23 2004

Revised definition from M. F. Hasler, Feb 24 2009

STATUS

approved