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• Pronic root is as if you say, 9 times 9 makes 81. And now take the root of 9, which is 3, and this 3 is added above 81: it makes 84, so that the pronic root of 84 is said to be 3.
• When a = 2, and d = 2 also, in this case, in equation 1st, s=n2 + n = a pronic number, which is produced by the addition of even numbers in an arithmetic progression beginning at 2; and the pronic root \scriptstyle n = \frac {\sqrt {4s +1} - 1}{2}.
• As I admire each proposition fair,
• the pronic number and the perfect square,
• the puzzling intricate equation solv'd,
• Thus, our search for cobalancing number is confined to the pronic triangular numbers, that is, triangular numbers that are also pronic numbers.
• It may be noted that if Ln is a pronic number, then Ln is two times a triangular number.
• A pronic number is that which is equal to the sum of a square number and its root. Thus, 6, 12, 20, 30, &c. are pronic numbers.