|
%I M0855 N0325 #50 Feb 13 2023 12:11:34
%S 2,3,7,23,41,71,191,409,2161,5881,36721,55441,71761,110881,760321,
%T 5109721,17551561,29418841,33358081,45024841,90441961,184254841,
%U 324013369,831143041,1685283601,6064561441,7111268641,9470788801,28725635761,108709927561,386681163961,1990614824641,44384069747161,89637484042681
%N Primes with record values of the least positive primitive root.
%D R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D 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. XLIV.
%H Michel Marcus, <a href="/A002230/b002230.txt">Table of n, a(n) for n = 1..38</a> (using McGown and Sorenson).
%H Stephen D. Cohen, Tomás Oliveira e Silva, and Tim Trudgian, <a href="http://arxiv.org/abs/1503.04519">On Grosswald's conjecture on primitive roots</a>, arXiv:1503.04519 [math.NT], 2015.
%H R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.
%H Kevin J. McGown and Jonathan P. Sorenson, <a href="https://arxiv.org/abs/2206.14193">Computation of the least primitive root</a>, arXiv:2206.14193 [math.NT], 2022.
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/p-roots.html#avg">Least prime primitive root of prime numbers</a>
%H A. E. Western and J. C. P. Miller, <a href="/A002223/a002223.pdf">Tables of Indices and Primitive Roots</a>, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]
%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%t s = {2}; rm = 1; Do[p = Prime[k]; r = PrimitiveRoot[p]; If[r > rm, Print[p]; AppendTo[s, p]; rm = r], {k, 10^6}]; s (* _Jean-François Alcover_, Apr 05 2011 *)
%t DeleteDuplicates[Table[{p,PrimitiveRoot[p,1]},{p,Prime[Range[61100]]}],GreaterEqual[ #1[[2]],#2[[2]]]&][[All,1]] (* The program generates the first 15 terms of the sequence. *) (* _Harvey P. Dale_, Aug 22 2022 *)
%o (Python)
%o from sympy import isprime, primitive_root
%o from itertools import count, islice
%o def f(n): return 0 if not isprime(n) or (r:=primitive_root(n))==None else r
%o def agen(r=0): yield from ((m, r:=f(m))[0] for m in count(1) if f(m) > r)
%o print(list(islice(agen(), 15))) # _Michael S. Branicky_, Feb 13 2023
%Y Cf. A002229 (for the primitive roots in question).
%Y Records in A023048, indices in A114885.
%K nonn,easy,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
|
