On Thu, 26 Mar 2009, James Buddenhagen wrote:
Numbers of the form n(n+1), where n is a positive integer are sometimes called "pronic numbers". See: http://en.wikipedia.org/wiki/Pronic_number However, in Sloane's OEIS both Richard Guy and Michael Somos say this is incorrect and it should be "promic numbers". See http://www.research.att.com/~njas/sequences/?q=2%2C6%2C12%2C20%2C30&sort=0&f...
I can't find either in any of my dictionaries. Which is correct? And what are the roots?
From: http://www.pballew.net/arithme2.html Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ... They are also called rectangular or oblong numbers. Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history. See also: http://tech.groups.yahoo.com/group/Hyacinthos/message/2466