Meaning of pronic | Babel Free

Definitions

Being the product of two consecutive integers.

not-comparable

Equivalents

Examples

“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.”

“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=(√4s+1-1)/2.”

“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”

“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.”

“It may be noted that if Lₙ is a pronic number, then Lₙ is two times a triangular number.”

“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.”

CEFR level