A029932 Primes with record values of the least positive prime primitive root.

3, 7, 23, 41, 109, 191, 271, 2791, 11971, 31771, 190321, 2080597, 3545281, 4022911, 73189117, 137568061, 443571241, 565822531, 1160260711, 1622723341, 31552100581, 81651092041, 96736641541, 1867622877121, 5000346134911

Offset

1,1

Comments

Other terms in the sequence: 39227234631271, 66597722601061 and 84054326426071 -Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008

Subsequence of A002230, considering only prime primitive roots. - M. F. Hasler, Jun 01 2018

References

R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.

A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XLV.

Links

Table of n, a(n) for n=1..25.

Tomás Oliveira e Silva, Counts of least primitive roots of prime numbers (Artin's conjecture)

Tomás Oliveira e Silva, Least prime primitive roots

A. Paszkiewicz and A. Schinzel, On the least prime primitive root modulo a prime, Math. Comp. 71 (2002), no. 239, 1307-1321.

A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]

Index entries for primes by primitive root

Mathematica

(* This program is not suitable for computing more than a dozen terms. *) max = 10^8; pprQ[r_, p_] := Union[Table[PowerMod[r, i, p], {i, 1, p+1}]] == coprimes; ppr[p_] := With[{spr = PrimitiveRoot[p]}, If[PrimeQ[spr], spr, coprimes = Select[Range[p-1], CoprimeQ[#, p]&]; For[r = NextPrime[ spr], True, r = NextPrime[r], If[pprQ[r, p], Return[r]]]]]; Reap[ For[ record=1; p=3, p<max, p = NextPrime[p], ppr1 = ppr[p]; If[ppr1 > record, record = ppr1; Print["p = ", p, " ppr = ", record]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Feb 25 2016 *)

Crossrefs

Cf. A060749, A002230, A084735.

Sequence in context: A053027 A133432 A133433 * A084739 A133434 A122870

Adjacent sequences: A029929 A029930 A029931 * A029933 A029934 A029935

Keyword

nonn,nice

Author

Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

Extensions

Corrected by Jud McCranie, Jan 04 2001

2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008

Status

approved