A350493 a(n) = floor(sqrt(prime(n)))^2 mod n.

0, 1, 1, 0, 4, 3, 2, 0, 7, 5, 3, 0, 10, 8, 6, 1, 15, 13, 7, 4, 1, 20, 12, 9, 6, 22, 19, 16, 13, 10, 28, 25, 22, 19, 4, 0, 33, 30, 27, 9, 5, 1, 40, 37, 16, 12, 8, 4, 29, 25, 21, 17, 13, 9, 36, 32, 28, 24, 20, 16, 12, 41, 37, 33, 29, 25, 56, 52, 48, 44, 40, 36

Offset

1,5

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = A065730(n) mod n.

Example

a(4) = A065730(4) mod 4 =  4 mod 4 = 0;
a(5) = A065730(5) mod 5 =  9 mod 5 = 4;
a(6) = A065730(6) mod 6 =  9 mod 6 = 3;
a(7) = A065730(7) mod 7 = 16 mod 7 = 2.

Mathematica

Table[PowerMod[Floor[Sqrt[Prime[n]]], 2, n], {n, 72}] (* Stefano Spezia, Jan 02 2022 *)

Prog

(PARI) a(n) = (sqrtint(prime(n))^2) % n;
vector(20, n, a(n))
(Ruby) require 'prime'
values = []
Prime.first(20).each_with_index do |prime, i|
    values << ((Integer.sqrt(prime) ** 2) % (i + 1))
end
p values
(Python)
from sympy import prime, integer_nthroot
def a(n): return (integer_nthroot(prime(n), 2)[0]**2)%n
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Jan 02 2022

Crossrefs

Cf. A000040, A048760, A065730.

Sequence in context: A258692 A067018 A200233 * A327351 A239475 A100802

Adjacent sequences: A350490 A350491 A350492 * A350494 A350495 A350496

Keyword

nonn

Author

Simon Strandgaard, Jan 01 2022

Status

approved