pronic

Etymology
Apparently from, a misspelling of , from , but the spelling has been from its earliest known occurrence in English ( Leonhard Euler, Opera Omnia, series 1, volume 15).

Adjective

 * 1)  Of a number which is the product of two consecutive integers
 * 2) * 1478 - Pierpaolo Muscharello, Algorismus p.163.
 * 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.
 * 1) * 1794 - David Wilkie, Theory of interest, p.6, Edinburgh: Peter Hill, 1794.
 * 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 $$\scriptstyle n = \frac {\sqrt {4s +1} - 1}{2}$$.
 * 1) * 1804 - Paul Deighan, "Recommendatory letters", A complete treatise on arithmetic, rational and practical, vol.1, p.viii, Dublin: J. Jones, 1804.
 * As I admire each proposition fair,
 * the pronic number and the perfect square,
 * the puzzling intricate equation solv'd,
 * as Grecia's chief the Gordian knot dissolv'd;
 * - John Bartley
 * 1) * 1814 - Charles Butler, Easy Introduction to Mathematics, p.96, Barlett & Newman, 1814
 * 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.
 * 1) * 2005 - G. K. Panda1 and P. K. Ray, "Cobalancing numbers and cobalancers", International Journal of Mathematics and Mathematical Sciences, vol.2005, iss.8, pp.1189-1200.
 * Thus, our search for cobalancing number is confined to the pronic triangular numbers, that is, triangular numbers that are also pronic numbers.
 * Thus, our search for cobalancing number is confined to the pronic triangular numbers, that is, triangular numbers that are also pronic numbers.

Translations

 * Finnish: proninen
 * German: pronisch
 * Polish: