A263651 Numbers n such that the difference between n and the largest square less than n is a nonzero square.

2, 5, 8, 10, 13, 17, 20, 26, 29, 34, 37, 40, 45, 50, 53, 58, 65, 68, 73, 80, 82, 85, 90, 97, 101, 104, 109, 116, 122, 125, 130, 137, 145, 148, 153, 160, 170, 173, 178, 185, 194, 197, 200, 205, 212, 221, 226, 229, 234, 241, 250, 257, 260, 265, 272, 281, 290, 293, 298, 305

Offset: 1

Author

Eli Jaffe, Oct 22 2015

Keywords

• nonn
• easy

Comments

Numbers n such that A053186(n) is a positive square. - Michel Marcus, Oct 23 2015

Numbers of the form a^2 + b^2 where a >= 1 and 1 <= b^2 <= 2a. - Robert Israel, Oct 23 2015

Numbers n such that A053610(n) = 2. - Thomas Ordowski, May 22 2016

Examples

			For n=5, the largest square less than 5 is 4, and the difference between 4 and 5 is 1, which is also square.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053186.

Programs

Maple

N:= 1000: # to get all terms <= N
sort([seq(seq(a^2 + b^2, b=1..min(floor(sqrt(2*a)),floor(sqrt(N-a^2)))),a=1..floor(sqrt(N-1)))]); # Robert Israel, Oct 23 2015

Mathematica

Select[Range@ 305, And[IntegerQ@ Sqrt[# - Floor[Sqrt@ #]^2], ! IntegerQ@ Sqrt@ #] &] (* Michael De Vlieger, Oct 23 2015 *)

PARI

isok(n) = (d = (n - sqrtint(n)^2)) && issquare(d); \\ Michel Marcus, Oct 23 2015

Extensions

More terms from Michel Marcus, Oct 23 2015