A277777 Largest nontrivial square root of unity modulo the n-th positive integer that does not have a primitive root (A033949).

5, 7, 11, 9, 11, 13, 19, 15, 19, 17, 23, 29, 19, 25, 31, 29, 23, 26, 41, 35, 27, 34, 43, 37, 49, 55, 33, 51, 43, 35, 47, 41, 55, 49, 39, 43, 53, 71, 71, 69, 59, 67, 71, 64, 47, 61, 56, 79, 89, 51, 67, 79, 76, 55, 89, 73, 97, 77, 91, 59, 64, 69, 109, 83, 63, 71

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Wikipedia, Root of unity modulo n

Formula

a(n) = A033949(n) - A082568(n).

Prog

(Python)
from gmpy2 import *
def f(n):
  for k in range(n - 2, 0, -1):
    if pow(k, 2, n) == 1:
      return k
def A277777(L):
  return [j for j in [f(k) for k in range(3, L + 1)] if j > 1] # Darío Clavijo, Oct 15 2022
(Python)
from itertools import count, islice
from sympy.ntheory import sqrt_mod_iter
def A277777_gen(): # generator of terms
    for n in count(3):
        if (m:=max(filter(lambda k:k<n-1, sqrt_mod_iter(1, n)))) > 1:
            yield m
A277777_list = list(islice(A277777_gen(), 30)) # Chai Wah Wu, Oct 26 2022

Crossrefs

Last elements of nonempty rows of A277776.

Cf. A033948, A033949, A082568.

Sequence in context: A096919 A023594 A357099 * A254930 A317769 A104200

Adjacent sequences: A277774 A277775 A277776 * A277778 A277779 A277780

Keyword

nonn,look

Author

Alois P. Heinz, Oct 30 2016

Status

approved