A002229 - OEIS

%I M0620 N0226 #40 Feb 13 2023 11:16:12

%S 1,2,3,5,6,7,19,21,23,31,37,38,44,69,73,94,97,101,107,111,113,127,137,

%T 151,164,179,194,197,227,229,263,281,293,335,347,359,401,417

%N Primitive roots that go with the primes in A002230.

%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 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 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]

%t s = {1}; rm = 1; Do[p = Prime[k]; r = PrimitiveRoot[p]; If[r > rm, Print[r]; AppendTo[s, r]; rm = r], {k, 10^6}]; s (* _Jean-François Alcover_, Apr 05 2011 *)

%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))[1] for m in count(1) if f(m) > r)

%o print(list(islice(agen(), 15))) # _Michael S. Branicky_, Feb 13 2023

%Y Cf. A002230.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_

%E More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

%E a(35)-a(38), from McGown and Sorenson, added by _Michel Marcus_, Jun 29 2022