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A002230
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Primes with record values of the least positive primitive root.
(Formerly M0855 N0325)
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6
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2, 3, 7, 23, 41, 71, 191, 409, 2161, 5881, 36721, 55441, 71761, 110881, 760321, 5109721, 17551561, 29418841, 33358081, 45024841, 90441961, 184254841, 324013369, 831143041, 1685283601, 6064561441, 7111268641, 9470788801, 28725635761, 108709927561, 386681163961, 1990614824641, 44384069747161, 89637484042681
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OFFSET
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1,1
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REFERENCES
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R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
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.
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LINKS
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MATHEMATICA
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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 *)
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 *)
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PROG
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(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))[0] for m in count(1) if f(m) > r)
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CROSSREFS
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Cf. A002229 (for the primitive roots in question).
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
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STATUS
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approved
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