A306252 Least primitive root mod A033948(n).

0, 1, 2, 3, 2, 5, 3, 2, 3, 2, 2, 3, 3, 5, 2, 7, 5, 2, 7, 2, 2, 3, 3, 2, 3, 6, 3, 5, 5, 3, 3, 2, 5, 3, 2, 2, 3, 2, 7, 5, 5, 3, 2, 7, 2, 3, 3, 5, 5, 3, 2, 5, 3, 2, 6, 3, 11, 2, 7, 2, 3, 2, 7, 3, 2, 7, 5, 2, 6, 5, 3, 5, 2, 5, 5, 2, 2, 3, 2, 2, 19, 5, 5, 2, 3, 3, 5

Offset

1,3

Comments

Let U(k) denote the multiplicative group mod k. a(n) = smallest generator for U(A033948(n)). - N. J. A. Sloane, Mar 10 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n=2, A033948(2) = 2, U(2) is generated by 1.
For n=14, A033948(14) = 18, and U(18) is generated by both 5 and 11; here we select the smallest generator, 5, so a(14) = 5.

Maple

0, op(subs(FAIL=NULL, map(numtheory:-primroot, [$2..1000]))); # Robert Israel, Mar 10 2019

Mathematica

Array[Take[PrimitiveRootList@ #, UpTo[1]] &, 210] // Flatten (* Michael De Vlieger, Feb 02 2019 *)

Prog

(Python)
from math import gcd
roots = [0]
for n in range(2, 140):
    # find U(n)
    un = [i for i in range(1, n) if gcd(i, n) == 1]
    # for each element in U(n), check if it's a generator
    order = len(un)
    is_cyclic = False
    for cand in un:
        is_gen = True
        run = 1
        # If it cand^x = 1 for some x < order, it's not a generator
        for _ in range(order-1):
            run = (run * cand) % n
            if run == 1:
                is_gen = False
                break
        if is_gen:
            roots.append(cand)
            is_cyclic = True
            break
print(roots)

Crossrefs

Cf. A033948 (numbers that have a primitive root), A306253, A081888 (positions of records), A081889 (record values). First column of A046147.

Sequence in context: A369029 A007967 A054494 * A112764 A108728 A331962

Adjacent sequences: A306249 A306250 A306251 * A306253 A306254 A306255

Keyword

nonn

Author

Charles Paul, Feb 01 2019

Extensions

More terms from Michael De Vlieger, Feb 02 2019

Edited by N. J. A. Sloane, Mar 10 2019

Edited by Robert Israel, Mar 10 2019

Status

approved