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

1,1

Links

Table of n, a(n) for n=1..80.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A256243, A256244.

Sequence in context: A154201 A355563 A332500 * A338151 A255642 A088701

Adjacent sequences: A253200 A253201 A253202 * A253204 A253205 A253206

Keyword

nonn,easy

Author

Tom Edgar and Zak Seidov, Mar 25 2015

Status

approved