A079060 Least k such that the least positive primitive root of prime(k) equals prime(n).

2, 4, 9, 20, 117, 88, 64, 43, 326, 1842, 775, 3894, 14401, 9204, 24092, 14837, 57481, 90901, 242495, 260680, 61005, 508929, 1084588, 436307, 1124509, 1824015, 2969632, 2052357, 4006960, 5241202, 10253662, 30802809, 17480124, 73915355, 98931475, 42664033

Offset

1,1

Comments

a(49) = 1247136427. For n > 45, a(n) > 1.5*10^9 except n = 49. - David A. Corneth, Feb 15 2023

Links

David A. Corneth, Table of n, a(n) for n = 1..45

Prog

(PARI) a(n) = {my(p=prime(n), s=1); while(p!=lift(znprimroot(prime(s))), s++); s; } \\ Modified by Jinyuan Wang, Apr 03 2020
(PARI) upto(u, {maxn = 100}) = { my(t = 1, m = Map(), res = []); forprime(p = 2, oo, mapput(m, p, t); t++; if(t > maxn, break ) ); t = 1; u = prime(u); forprime(p = 2, u, c = lift(znprimroot(p)); if(mapisdefined(m, c), ind = mapget(m, c); if(ind > #res, res = concat(res, vector(ind - #res)) ); if(res[ind] == 0, res[ind] = t; ) ); t++ ); res } \\ David A. Corneth, Feb 15 2023
(Python)
from sympy import nextprime, primitive_root
def a(n):
    k, pk, pn = 1, 2, prime(n)
    while primitive_root(pk) != pn: k += 1; pk = nextprime(pk)
    return k
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Feb 13 2023
(Python) # faster version for segments of sequence
from itertools import count, islice
from sympy import isprime, nextprime, prime, primepi, primitive_root
def agen(startk=1, startn=1): # generator of terms
    p, vdict, adict, n = prime(startk), dict(), dict(), startn
    for k in count(startk):
        v = primitive_root(p)
        if v not in vdict and isprime(v):
            vdict[v] = k
            adict[primepi(v)] = k
        while n in adict: yield adict[n]; n += 1
        p = nextprime(p)
print(list(islice(agen(), 18))) # Michael S. Branicky, Feb 14 2023

Crossrefs

Cf. A001918, A023048, A066529.

Sequence in context: A264293 A370315 A034750 * A225173 A346737 A030039

Adjacent sequences: A079057 A079058 A079059 * A079061 A079062 A079063

Keyword

nonn

Author

Benoit Cloitre, Feb 02 2003

Extensions

a(17)-a(18) from Jinyuan Wang, Apr 03 2020

a(19)-a(36) from Michael S. Branicky, Feb 14 2023

Status

approved