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A350493
a(n) = floor(sqrt(prime(n)))^2 mod n.
0
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
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
KEYWORD
nonn
AUTHOR
Simon Strandgaard, Jan 01 2022
STATUS
approved