A129861 Smallest square s such that A024352(n) + s is square.

1, 4, 9, 1, 16, 25, 4, 36, 1, 9, 64, 81, 16, 4, 121, 1, 144, 9, 36, 196, 225, 4, 16, 1, 64, 324, 25, 9, 400, 441, 100, 4, 529, 1, 576, 49, 144, 676, 9, 25, 64, 841, 4, 900, 1, 36, 16, 1089, 256, 100, 1225, 49, 1296, 25, 324, 4, 1521, 81, 144, 1681, 16, 36, 169, 81, 1936, 9, 484

Offset: 1

Author

Andrew S. Plewe, May 23 2007

Keywords

• nonn

Examples

			5(5+6) = 55, smallest square = (6/2)^2 = 9
4(4+10) = 56, smallest square = (10/2)^2 = 25
3(3+16) = 57, smallest square = (16/2)^2 = 64
1(1+58) = 59, smallest square = (58/2)^2 = 841
6(6+4) = 60, smallest square = (4/2)^2 = 4
1(1+60) = 61, smallest square = (60/2)^2 = 900
7(7+2) = 63, smallest square = (2/2)^2 = 1
etc.
		

Crossrefs

Cf. A024352.

Formula

y(y+e) = A024352(n), where e is the smallest even number that satisfies this equation, A(n) = (e/2)^2.