OFFSET
1,1
COMMENTS
n is a "congruum" iff n/4 is the area of a Pythagorean triangle, so these are the numbers 4*A009112.
Each congruum is a multiple of 24; it cannot be a square.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Congruum (but beware errors)
Wikipedia, Congruum (but beware errors).
EXAMPLE
a(11)=840 since 840=29^2-1^2=41^2-29^2 (indeed also 840=37^2-23^2=47^2-37^2).
MATHEMATICA
r[n_] := Reduce[0 < y < x && 0 < x < z && n == x^2 - y^2 == z^2 - x^2, {x, y, z}, Integers];
Reap[For[n = 24, n < 10^4, n += 24, rn = r[n]; If[rn =!= False, Print[n, " ", rn]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 25 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 06 2015, following a suggestion from Robert Israel, Apr 03. 2015. This entry incorporates many comments that were originally in A057102. A057103 and A055096 need to be checked.
STATUS
approved