A079060 - OEIS

%I #25 Feb 16 2023 05:23:04

%S 2,4,9,20,117,88,64,43,326,1842,775,3894,14401,9204,24092,14837,57481,

%T 90901,242495,260680,61005,508929,1084588,436307,1124509,1824015,

%U 2969632,2052357,4006960,5241202,10253662,30802809,17480124,73915355,98931475,42664033

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

%C a(49) = 1247136427. For n > 45, a(n) > 1.5*10^9 except n = 49. - _David A. Corneth_, Feb 15 2023

%H David A. Corneth, <a href="/A079060/b079060.txt">Table of n, a(n) for n = 1..45</a>

%o (PARI) a(n) = {my(p=prime(n), s=1); while(p!=lift(znprimroot(prime(s))), s++); s; } \\ Modified by _Jinyuan Wang_, Apr 03 2020

%o (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

%o (Python)

%o from sympy import nextprime, primitive_root

%o def a(n):

%o     k, pk, pn = 1, 2, prime(n)

%o     while primitive_root(pk) != pn: k += 1; pk = nextprime(pk)

%o     return k

%o print([a(n) for n in range(1, 19)]) # _Michael S. Branicky_, Feb 13 2023

%o (Python) # faster version for segments of sequence

%o from itertools import count, islice

%o from sympy import isprime, nextprime, prime, primepi, primitive_root

%o def agen(startk=1, startn=1): # generator of terms

%o     p, vdict, adict, n = prime(startk), dict(), dict(), startn

%o     for k in count(startk):

%o         v = primitive_root(p)

%o         if v not in vdict and isprime(v):

%o             vdict[v] = k

%o             adict[primepi(v)] = k

%o         while n in adict: yield adict[n]; n += 1

%o         p = nextprime(p)

%o print(list(islice(agen(), 18))) # _Michael S. Branicky_, Feb 14 2023

%Y Cf. A001918, A023048, A066529.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 02 2003

%E a(17)-a(18) from _Jinyuan Wang_, Apr 03 2020

%E a(19)-a(36) from _Michael S. Branicky_, Feb 14 2023