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Numbers n such that there are seven distinct triples (k, k+n, k+2n) of squares.
1

%I #16 Sep 07 2013 09:46:41

%S 12671122464000,50684489856000,114040102176000,202737959424000,

%T 316778061600000,456160408704000,620885000736000,810951837696000,

%U 1026360919584000,1267112246400000,1533205818144000

%N Numbers n such that there are seven distinct triples (k, k+n, k+2n) of squares.

%C For the first 11 terms we have a(n) = n^2 * a(1). Are there any other primitive terms other than a(1)?

%e These 7 triples of squares have a common difference of 12671122464000: (676403^2, 3623347^2, 5079347^2), (911820^2, 3674580^2, 5116020^2), (2615340^2, 4417140^2, 5672940^2), (4885860^2, 6045060^2, 7015260^2), (5664815^2, 6690385^2, 7578415^2), (10873380^2, 11441220^2, 11982180^2) and (11985330^2, 12502770^2, 12999630^2).

%Y Cf. A198387, A222154, A222155, A214155, A226858.

%K nonn

%O 1,1

%A _Zdenek Cervenka_, Jun 26 2013