A253203 The least square larger than n with same parity as n.

9, 4, 9, 16, 9, 16, 9, 16, 25, 16, 25, 16, 25, 16, 25, 36, 25, 36, 25, 36, 25, 36, 25, 36, 49, 36, 49, 36, 49, 36, 49, 36, 49, 36, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 49, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 64, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100, 81, 100

Offset: 1

Author

Tom Edgar and Zak Seidov, Mar 25 2015

Keywords

• nonn
• easy

Examples

			9 is the least odd square > 1;
4 is the least even square > 2;
9 is the least odd square > 3.
		

Crossrefs

Cf. A256243, A256244.

Programs

Mathematica

f[n_] := Block[{s = If[n == 1, Range[3]^2, Range[2 Ceiling@ Sqrt@ n]^2]}, If[EvenQ@ n, SelectFirst[s, EvenQ@ # && # > n &], SelectFirst[s, OddQ@ # && # > n &]]]; Array[f, 120] (* Michael De Vlieger, Mar 25 2015 *)

Sage

A = []
for i in [1..100]:
    for y in [1..100]:
        x = y**2
        if x>i and (x-i)%2==0:
            A.append(x)
            break
A

Formula

a(n) = A256244(n)^2 = n + 2*A256243(n).