A001125 -id:A001125 - cp's OEIS frontend

A063939 Numbers p from A001125 such that 2*p-3 is prime.

41, 251, 991, 1471, 2551, 3301, 4211, 4721, 4931, 5167, 5581, 5791, 7351, 8317, 8581, 9157, 9781, 11701, 12517, 13093, 15541, 16741, 16927, 17341, 18301, 18397, 19121, 19231, 20411, 22571, 23911, 24151, 25741, 26293, 26317, 26681, 27031

Offset: 1

Jason Earls, Aug 31 2001

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A001125.

j=[]; forprime(p=3,40000, if(znprimroot(p)==6, if(isprime(2*p- 3),j=concat(j,p)))); j

{ n=0; p=0; for (m=1, 10^9, p=nextprime(p+1); if (znprimroot(p)==6 && isprime(2*p - 3), write("b063939.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 03 2009

A001124 Primes with 5 as smallest primitive root.

Original entry on oeis.org

23, 47, 73, 97, 103, 157, 167, 193, 263, 277, 307, 383, 397, 433, 503, 577, 647, 673, 683, 727, 743, 863, 887, 937, 967, 983, 1033, 1093, 1103, 1153, 1163, 1223, 1367, 1487, 1543, 1583, 1607, 1777, 1823, 1847, 1933, 1993, 2003, 2017, 2063, 2087, 2113, 2203, 2207

Offset: 1

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 57.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for primes by primitive root

Cf. A001122, A001123, A001125, etc.

<< NumberTheory`NumberTheoryFunctions`; Prime[ Select[ Range[200], PrimitiveRoot[ Prime[ # ] ] == 5 & ] ]
(* first load *) << NumberTheory`NumberTheoryFunctions` (* then *) Select[ Prime@Range@300, PrimitiveRoot@# == 5 &] (* Robert G. Wilson v, May 11 2001 *)
Select[Prime[Range[350]],PrimitiveRoot[#]==5&] (* The PrimitiveRoot function is now part of Mathematica's core, so no add-in needs to be loaded before calling it *) (* Harvey P. Dale, Dec 06 2014 *)

from itertools import islice
from sympy import nextprime, primitive_root
def A001124_gen(): # generator of terms
    p = 5
    while (p:=nextprime(p)):
        if primitive_root(p)==5:
            yield p
A001124_list = list(islice(A001124_gen(),30)) # Chai Wah Wu, Feb 13 2023

More terms from Robert G. Wilson v, May 10 2001

A072190 Indices of primes with primitive root 2.

Original entry on oeis.org

2, 3, 5, 6, 8, 10, 12, 16, 17, 18, 19, 23, 26, 28, 32, 34, 35, 38, 40, 41, 42, 45, 47, 49, 57, 62, 66, 69, 70, 74, 75, 77, 81, 82, 86, 89, 91, 94, 97, 99, 100, 101, 102, 103, 107, 112, 114, 119, 120, 121, 123, 126, 127, 134, 137, 138, 139, 142, 144, 145, 147

Offset: 1

Miklos Kristof, Jul 02 2002

Artin conjectured that this sequence is infinite (this is the famous Artin Conjecture).

			8 is an element of the sequence: 19 the 8th prime and 2 is primitive root of 19. 9 is not element of the sequence, since 23 is the 9th prime and 2 is not primitive root of 23.

M. Abramowitz and I.A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, New York, 1996. see p. 169
L. Huber, manuscripts on Group Theory and Number Theory, 1990-1995

T. D. Noe, Table of n, a(n) for n = 1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Artin's conjecture

Cf. A001122, A001123, A001124, A001125.

Select[Range[300], MultiplicativeOrder[2, Prime[#]] == Prime[#] - 1 &] (* T. D. Noe, Apr 16 2014 *)

Edited by N. J. A. Sloane, Apr 11 2009

Extended by T. D. Noe, Apr 16 2014

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A063939 Numbers p from A001125 such that 2*p-3 is prime.

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A001124 Primes with 5 as smallest primitive root.

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A072190 Indices of primes with primitive root 2.

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