A067722 Least positive integer k such that n*(n + k) is a perfect square.

1, 3, 6, 9, 5, 15, 18, 21, 10, 7, 30, 33, 15, 39, 42, 45, 9, 51, 14, 57, 25, 63, 66, 69, 30, 11, 78, 21, 35, 87, 90, 93, 18, 99, 102, 105, 13, 111, 114, 117, 50, 123, 126, 129, 55, 35, 138, 141, 27, 15, 22, 153, 65, 159, 42, 165, 70, 171, 174, 177, 75, 183, 186, 49, 17

Offset: 0

Author

Robert G. Wilson v, Feb 05 2002

Keywords

• nonn

Examples

			a(8) = 10 because 8*(8+10) = 144 = 12^2.
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A010052.

Programs

Haskell

a067722 n = head [k | k <- [1..], a010052 (n * (n + k)) == 1]
-- Reinhard Zumkeller, Feb 07 2015

Mathematica

Do[k = 1; While[ !IntegerQ[ Sqrt[ k (k + n)]], k++ ]; Print[k], {n, 0, 75} ]

PARI

a(n) = my(k=1); while(!issquare(n*(n+k)), k++); k; \\ Michel Marcus, Feb 05 2015