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A001124
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Primes with 5 as smallest primitive root.
(Formerly M5132 N2224)
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6
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23, 47, 73, 97, 103, 157, 167, 193, 263, 277, 307, 383, 397, 433, 503, 577, 647, 673, 683, 727, 743, 863, 887, 937, 967, 983, 1033, 1093, 1103, 1153, 1163, 1223, 1367, 1487, 1543, 1583, 1607, 1777, 1823, 1847, 1933, 1993, 2003, 2017, 2063, 2087, 2113, 2203, 2207
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 57.
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).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions`; Prime[ Select[ Range[200], PrimitiveRoot[ Prime[ # ] ] == 5 & ] ]
(* first load *) << NumberTheory`NumberTheoryFunctions` (* then *) Select[ Prime@Range@300, PrimitiveRoot@# == 5 &] (* Robert G. Wilson v, May 11 2001 *)
Select[Prime[Range[350]], PrimitiveRoot[#]==5&] (* The PrimitiveRoot function is now part of Mathematica's core, so no add-in needs to be loaded before calling it *) (* Harvey P. Dale, Dec 06 2014 *)
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PROG
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(Python)
from itertools import islice
from sympy import nextprime, primitive_root
def A001124_gen(): # generator of terms
p = 5
while (p:=nextprime(p)):
if primitive_root(p)==5:
yield p
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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