A338227 a(n) = x(n) mod floor(sqrt(x(n))), where x(n) = floor((n^2)/2).

0, 0, 0, 0, 2, 0, 2, 4, 1, 4, 0, 3, 8, 2, 7, 0, 6, 11, 4, 10, 2, 8, 0, 6, 14, 3, 12, 0, 9, 18, 6, 15, 2, 12, 23, 8, 20, 4, 16, 0, 12, 24, 7, 20, 2, 15, 30, 10, 25, 4, 20, 35, 14, 30, 8, 24, 1, 18, 36, 11, 30, 4, 23, 42, 16, 35, 8, 28, 0, 20, 42, 12, 34, 3

Offset

2,5

Links

Table of n, a(n) for n=2..75.

Simon Strandgaard, Plot of 10000 terms with primes highlighted

Formula

a(n) = A007590(n) mod A000196(A007590(n)).

a(n) = A007590(n) mod A049472(n). - Kevin Ryde, Jan 30 2021

Example

x( 7) = floor(( 7^2)/2) = 24, a( 7) = 24 mod floor(sqrt(24)) = 24 mod 4 = 0,
x( 8) = floor(( 8^2)/2) = 32, a( 8) = 32 mod floor(sqrt(32)) = 32 mod 5 = 2,
x( 9) = floor(( 9^2)/2) = 40, a( 9) = 40 mod floor(sqrt(40)) = 40 mod 6 = 4,
x(10) = floor((10^2)/2) = 50, a(10) = 50 mod floor(sqrt(50)) = 50 mod 7 = 1.

Mathematica

x[n_] := Floor[(n^2)/2]; A338227[n_] := Mod[x[n], Floor[Sqrt[x[n]]]]; Table[A338227[n], {n, 2, 75}] (* Robert P. P. McKone, Jan 31 2021 *)

Prog

(Ruby) values = Array.new(50) do |i|
    x = ((i + 2) ** 2) / 2
    x % Integer.sqrt(x)
end
p values
(PARI) a(n) = my(x=n^2\2); x % sqrtint(x); \\ Michel Marcus, Jan 31 2021

Crossrefs

Cf. A000196, A007590, A049472.

Sequence in context: A092594 A092741 A347223 * A350861 A144182 A037036

Adjacent sequences: A338224 A338225 A338226 * A338228 A338229 A338230

Keyword

nonn

Author

Simon Strandgaard, Jan 30 2021

Status

approved