A002229 Primitive roots that go with the primes in A002230. (Formerly M0620 N0226)

1, 2, 3, 5, 6, 7, 19, 21, 23, 31, 37, 38, 44, 69, 73, 94, 97, 101, 107, 111, 113, 127, 137, 151, 164, 179, 194, 197, 227, 229, 263, 281, 293, 335, 347, 359, 401, 417

Offset

1,2

References

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).

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.

Links

Table of n, a(n) for n=1..38.

R. K. Guy and N. J. A. Sloane, Correspondence, 1988.

Kevin J. McGown and Jonathan P. Sorenson, Computation of the least primitive root, arXiv:2206.14193 [math.NT], 2022.

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]

Mathematica

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 *)

Prog

(Python)
from sympy import isprime, primitive_root
from itertools import count, islice
def f(n): return 0 if not isprime(n) or (r:=primitive_root(n))==None else r
def agen(r=0): yield from ((m, r:=f(m))[1] for m in count(1) if f(m) > r)
print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 13 2023

Crossrefs

Cf. A002230.

Sequence in context: A073721 A285639 A090745 * A299158 A146747 A077674

Adjacent sequences: A002226 A002227 A002228 * A002230 A002231 A002232

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

a(35)-a(38), from McGown and Sorenson, added by Michel Marcus, Jun 29 2022

Status

approved