OFFSET
1,1
COMMENTS
These are n and k such that the generalized Pell equation (k-2)*x^2 - (k-4)*x = (n-2)*y^2 - (n-4)*y has no solution in integers x>1 and y>1. The paper by Chu shows how to solve these equations. A necessary condition for a pair to be in this sequence is (n-2)(k-2) is a square. These (n,k) pairs indicate where the zeros are in triangle A189216, which gives the least n-gonal k-gonal number greater than 1. For triangular (n=3) and square (n=4) numbers, see A188892 and A188896 for lists of k.
LINKS
Wenchang Chu, Regular polygonal numbers and generalized Pell equations, Int. Math. Forum 2 (2007), 781-802.
Eric W. Weisstein, MathWorld: Polygonal Number
EXAMPLE
The pairs begin (3,11), (4,10), (6,11), (5,14), (3,18), (4,20), (6,18).
MATHEMATICA
maxSum=100; Reap[Do[k=s-n; If[k>n && IntegerQ[Sqrt[(n-2)*(k-2)]] && FindInstance[(k-2)*x^2 - (k-4)*x == (n-2)*y^2 - (n-4)*y && x>1 && y>1, {x, y}, Integers] == {}, Sow[{n, k}]], {s, 7, maxSum}, {n, 3, s-3}]][[2, 1]]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Apr 20 2011
STATUS
approved