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A193800 Least m > 0 such that (n+m)^2 - m^2 (= n^2 + 2*m*n) is a square. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)