A336302 a(n) = n^2 mod ceiling(sqrt(n)).

0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 4, 4, 1, 0, 1, 4, 4, 1, 0, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 4, 2, 2, 4, 1, 0, 1, 4, 2, 2, 4, 1, 0, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 4, 9, 5, 3, 3, 5, 9, 4

Offset: 1

Author

William Phoenix Marcum, Oct 05 2020

Keywords

• nonn
• easy
• look

Comments

A pattern emerges for certain values where ceiling(sqrt(n)) is the same.

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000
• William Marcum, Desmos graph

Crossrefs

Cf. A000290, A003059.

Programs

Mathematica

Table[Mod[n^2, Ceiling @ Sqrt[n]], {n, 100}] (* Amiram Eldar, Oct 05 2020 *)

PARI

a(n) = lift(Mod(n, ceil(sqrt(n)))^2); \\ Michel Marcus, Oct 05 2020

Formula

a(n) = A000290(n) mod A003059(n). - Michel Marcus, Oct 05 2020

a(n^2) = 0. - Michel Marcus, Oct 07 2020