OFFSET
1,1
COMMENTS
Least m > 0 for which x^2 - m*y^2 = 1 has a solution with y = n.
For n > 1, a(n) <= n^2-2. - Chai Wah Wu, Jan 26 2016
LINKS
T. D. Noe and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..500 from T. D. Noe
FORMULA
For n a power of an odd prime, a(n) = n^2 - 2. For n twice a power of an odd prime, a(n) = (n/2)^2 - 1. - T. D. Noe, Sep 13 2007
EXAMPLE
a(4)=3, based on 3*4^2 + 1 = 7^2.
MATHEMATICA
a[n_] := For[m=1, True, m++, If[IntegerQ[Sqrt[m*n^2+1]], Return[m]]]; Table[a[n], {n, 100}]
lm[n_]:=Module[{m=1}, While[!IntegerQ[Sqrt[m n^2+1]], m++]; m]; Array[lm, 60] (* Harvey P. Dale, Feb 24 2013 *)
PROG
(Haskell)
a067872 n = (until ((== 1) . a010052 . (+ 1)) (+ nn) nn) `div` nn
where nn = n ^ 2
-- Reinhard Zumkeller, Jun 28 2013
(Python)
def A067872(n):
y, x, n2 = n*(n+2), 2*n+3, n**2
m, r = divmod(y, n2)
while r:
y += x
x += 2
m, r = divmod(y, n2)
return m # Chai Wah Wu, Jan 25 2016
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Lekraj Beedassy, Feb 25 2002
EXTENSIONS
Edited by Dean Hickerson, Mar 19 2002
STATUS
approved