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A096910
Primitive Pythagorean Quadruples a^2+b^2+c^2=d^2, 0<a<=b<=c<=d, gcd(a,b,c,d)=1, sorted by d, then c, then b; sequence gives d values.
9
3, 7, 9, 9, 11, 11, 13, 15, 15, 17, 17, 19, 19, 19, 21, 21, 21, 21, 23, 23, 23, 25, 25, 27, 27, 27, 27, 27, 29, 29, 29, 31, 31, 31, 31, 33, 33, 33, 33, 33, 33, 33, 35, 35, 35, 35, 37, 37, 37, 37, 39, 39, 39, 39, 39, 39, 41, 41, 41, 41, 41, 43, 43, 43, 43, 43, 43, 45, 45, 45
OFFSET
1,1
COMMENTS
Sequence with repetitions removed is A005818. - Ivan Neretin, May 24 2015
LINKS
Eric Weisstein's World of Mathematics, Pythagorean Quadruple.
MATHEMATICA
mx = 50; res = {}; Do[If[GCD[b, c, d] > 1, Continue[]]; If[IntegerQ[a = Sqrt[d^2 - b^2 - c^2]] && a > 0 && a <= b, AppendTo[res, {a, b, c, d}]], {d, mx}, {c, d}, {b, c}]; res[[All, 4]] (* Ivan Neretin, May 24 2015 *)
CROSSREFS
Cf. A096907, A096908, A096909 (other components of the quadruple), A046086, A046087, A020882 (Pythagorean triples ordered in a similar way).
Sequence in context: A347926 A331066 A179021 * A182389 A279615 A169968
KEYWORD
nonn
AUTHOR
Ray Chandler, Aug 15 2004
STATUS
approved