2,1

"You can find an infinite number of [different] triangular numbers such that when multipled together form a square number. For example, for every triangular number, T_n, there are an infinite number of other triangular numbers, T_m, such that T_n*T_m is a square. For example, T_2 * T_24 = 30^2."

Clifford A. Pickover, The Loom of God, Tapestries of Mathematics and Mysticism, Sterling, NY, 2009, page 33.

tri[n_] := n (n + 1)/2; f[n_] := Block[{k = n + 1, t = tri@n}, While[ !IntegerQ@ Sqrt[ t*tri@k], k++ ]; k]; Table[ f@n, {n, 2, 46}]

Cf. A132596, A007654, A132584.

Sequence in context: A288639 A280097 A054734 * A029613 A083541 A230761

Adjacent sequences: A174903 A174904 A174905 * A174907 A174908 A174909

Robert G. Wilson v, Apr 01 2010

approved