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

1,17

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000290, A003059.

Sequence in context: A048152 A350037 A070430 * A163353 A164612 A309748

Adjacent sequences: A336299 A336300 A336301 * A336303 A336304 A336305

Keyword

nonn,easy,look

Author

William Phoenix Marcum, Oct 05 2020

Status

approved