A002229 Primitive roots that go with the primes in A002230.

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

Author

N. J. A. Sloane

Keywords

• nonn
• more

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

• 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]

Crossrefs

Cf. A002230.

Programs

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 *)

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

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