pronic

English

Etymology

Apparently from New Latin pronicus, a misspelling of Latin promicus, from Ancient Greek προμήκης (promḗkēs, “elongated, oblong”), but the spelling has been pronic from its earliest known occurrence in English (

(Can we date this quote?) Leonhard Euler, Opera Omnia, series 1, volume 15).

Pronunciation

• IPA^(key): /ˈpɹɒnɪk/

Adjective

pronic (not comparable)

1. (mathematics) Of a number which is the product of two consecutive integers
   • 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 $\scriptstyle n={\frac {{\sqrt {4s+1}}-1}{2}}$.

   • 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

   • 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.

   • 1998, Wayne L. McDaniel, “Pronic Lucas Numbers”, in The Fibonacci Quarterly, pages 60–62:

     It may be noted that if L_n is a pronic number, then L_n 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.

Synonyms

• heteromecic

Related terms

• rectangular number
• oblong number

Translations

Translations

• Finnish: proninen
• French: pronique (fr), oblong (fr), hétéromécique (fr)
• German: pronisch
• Polish: not used in Polish