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

Author

Charles Paul, Feb 01 2019

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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)

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