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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A053186.

Sequence in context: A172000 A096691 A202057 * A070216 A100829 A030713

Adjacent sequences: A263648 A263649 A263650 * A263652 A263653 A263654

Keyword

nonn,easy

Author

Eli Jaffe, Oct 22 2015

Extensions

More terms from Michel Marcus, Oct 23 2015

Status

approved