A193800 Least m > 0 such that (n+m)^2 - m^2 (= n^2 + 2*m*n) is a square.

4, 3, 12, 6, 20, 9, 28, 5, 8, 15, 44, 18, 52, 21, 60, 10, 68, 7, 76, 30, 84, 33, 92, 15, 12, 39, 24, 42, 116, 45, 124, 9, 132, 51, 140, 14, 148, 57, 156, 25, 164, 63, 172, 66, 40, 69, 188, 30, 16, 11, 204, 78, 212, 21, 220, 35, 228, 87, 236, 90, 244, 93, 56, 18

Offset

1,1

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Example

a(1)=4 is the smallest positive integer such that 1^2+2*1*a(1) is a square, here 1+2*4 = 3^2.
a(2)=3 is the smallest positive integer such that 2^2+2*2*a(2) is a square, here 4+4*3 = 4^2.
a(3)=12 is the smallest positive integer such that 3^2+2*3*a(3) is a square, here 9+6*12 = 9^2.

Mathematica

f[n_] := Block[{k = 1}, While[ !IntegerQ[ Sqrt[ n^2 + 2 n*k]], k++]; k]; Array[f, 64] (* Robert G. Wilson v, Jun 05 2014 *)

Prog

(PARI) a(n)=for(m=1, 1e9, issquare((n+m)^2-m^2)&return(m))
(Magma)
S:=[];
m:=1;
for n in [1..65] do
   while not IsSquare((n+m)^2-m^2) do
        m:=m+1;
   end while;
   Append(~S, m);
   m:=1;
end for;
S;  // Bruno Berselli, Jan 29 2013

Crossrefs

Sequence in context: A091512 A106285 A240134 * A061727 A327916 A270025

Adjacent sequences: A193797 A193798 A193799 * A193801 A193802 A193803

Keyword

nonn

Author

M. F. Hasler, Aug 05 2011

Status

approved