A174906 - OEIS

A174906

a(n) is the index of the first triangular number T_i exceeding T_n such that the product of T_i*T_n is a perfect square.

24, 48, 80, 120, 168, 224, 49, 360, 440, 528, 624, 728, 840, 960, 1088, 1224, 1368, 1520, 1680, 1848, 2024, 2208, 242, 2600, 2808, 3024, 3248, 3480, 3720, 3968, 4224, 4488, 4760, 5040, 5328, 5624, 5928, 6240, 6560, 6888, 7224, 7568, 7920, 8280, 8648

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OFFSET

2,1

COMMENTS

"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."

REFERENCES

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

LINKS

Table of n, a(n) for n=2..46.

MATHEMATICA

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}]

CROSSREFS

Cf. A132596, A007654, A132584.

Sequence in context: A288639 A280097 A054734 * A029613 A083541 A230761

Adjacent sequences: A174903 A174904 A174905 * A174907 A174908 A174909

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Apr 01 2010

STATUS

approved