A227453 Numbers k such that the distance to the largest square less than k is a multiple of 4.

8, 13, 20, 24, 29, 33, 40, 44, 48, 53, 57, 61, 68, 72, 76, 80, 85, 89, 93, 97, 104, 108, 112, 116, 120, 125, 129, 133, 137, 141, 148, 152, 156, 160, 164, 168, 173, 177, 181, 185, 189, 193, 200, 204, 208, 212, 216, 220, 224, 229, 233, 237, 241, 245, 249, 253, 260, 264, 268, 272, 276, 280

Offset

1,1

Comments

A071797(a(n)) = 4*m, A053186(a(n)+1) = 4*m, m > 0.

Apparently a bisection of A079896. While it may not be difficult to prove that the sequence is a subsequence of A079896, the apparent fact that a(n) = A079896(2n-1) is by no means obvious.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

8 - 2^2 = 1*4 and 24 - 4^2 = 2*4 so 8 and 24 are in the sequence.

Mathematica

lsm4Q[n_]:=Module[{s=Floor[Sqrt[n]]^2}, s<n&&Divisible[n-s, 4]]; Select[ Range[300], lsm4Q] (* Harvey P. Dale, Jun 20 2014 *)

Prog

(PARI) is(n)=(n-sqrtint(n-1)^2)%4==0

Crossrefs

Cf. A048760, A053186, A071797, A079896.

Sequence in context: A030782 A219721 A176209 * A266212 A063849 A273980

Adjacent sequences: A227450 A227451 A227452 * A227454 A227455 A227456

Keyword

nonn

Author

Ralf Stephan, Sep 22 2013

Status

approved