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A248943 Sum of squares of diagonals of a parallelogram (but not rectangle or rhombus) with integer sides and diagonals and their GCD is 1. 0
130, 170, 250, 260, 290, 340, 370, 410, 442, 500, 530, 580, 610, 650, 650, 650, 730, 740, 754, 820, 850, 850, 850, 884, 890, 962, 970, 986, 1010, 1060, 1066, 1090, 1130, 1220, 1250, 1258, 1300, 1300, 1300, 1370, 1378, 1394, 1450, 1450, 1450, 1460, 1490, 1508, 1570, 1586, 1690, 1690, 1690, 1700, 1700, 1700, 1730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Alternate definition: Lists of P satisfying P = 2a^2 + 2b^2 = c^2 + d^2 (by parallelogram law) and a + b > max(c,d) (by triangle inequality) and a!=b (removes rhombus) and c!=d (removes rectangle) and gcd(a,b,c,d)=1.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

a...b...c...d...P=2a^2+2b^2=c^2+d^2

4...7...7...9...130

6...7...7...11..170

5...10..9...13..250

7...9...8...14..260

8...9...11..13..290

7...11..12..14..340

8...11..9...17..370

6...13..11..17..410

10..11..9...19..442

9...13..10..20..500

MATHEMATICA

PMax=2000;

Do[Sqrt[P/2-a^2]//If[IntegerQ[#]&&GCD[a, #, c[[1]], c[[2]]]==1, P//Sow]&, {P, 2, PMax, 2}, {c, DeleteCases[PowersRepresentations[P, 2, 2], {x_, x_}]}, {a, (c[[2]]-c[[1]])/2+1, Sqrt[P]/2-1//Ceiling}]//Reap//Last//Last

CROSSREFS

Sequence in context: A252369 A252362 A331629 * A248649 A050238 A115937

Adjacent sequences:  A248940 A248941 A248942 * A248944 A248945 A248946

KEYWORD

nonn

AUTHOR

Albert Lau, Oct 17 2014

STATUS

approved

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Last modified August 13 20:49 EDT 2022. Contains 356107 sequences. (Running on oeis4.)