A081888 -id:A081888 - cp's OEIS frontend

A081889 Least primitive root corresponding to A081888(n).

1, 2, 3, 5, 7, 11, 19, 21, 23, 31, 35, 41, 43, 53, 57, 69, 87, 93, 95, 101, 115, 141, 173, 203

Offset: 1

Sven Simon, Mar 30 2003

from sympy import primitive_root
from itertools import count, islice
def f(n): r = primitive_root(n); return r if r != None else 0
def agen(r=0): yield from ((m, r:=f(m))[1] for m in count(1) if f(m) > r)
print(list(islice(agen(), 18))) # Michael S. Branicky, Feb 13 2023

a(24) from Michael S. Branicky, Feb 20 2023

A306252 Least primitive root mod A033948(n).

Original entry on oeis.org

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

Charles Paul, Feb 01 2019

nonn

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

			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.

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

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

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

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

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)

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

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A081889 Least primitive root corresponding to A081888(n).

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A306252 Least primitive root mod A033948(n).

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