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Search: id:A001918
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| A001918 |
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Least positive primitive root of n-th prime.
(Formerly M0242 N0083)
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+0
68
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| 1, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 6, 3, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 5, 2, 6, 3, 3, 2, 3, 2, 2, 6, 5, 2, 5, 2, 2, 2, 19, 5, 2, 3, 2, 3, 2, 6, 3, 7, 7, 6, 3, 5, 2, 6, 5, 3, 3, 2, 5, 17, 10, 2, 3, 10, 2, 2, 3, 7, 6, 2, 2, 5, 2, 5, 3, 21, 2, 2, 7, 5, 15, 2, 3, 13, 2, 3, 2, 13, 3, 2, 7, 5, 2, 3, 2, 2, 2, 2, 2, 3
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 213.
CRC Handbook of Combinatorial Designs, 1996, p. 615.
P. Fan and M. Darnell, Sequence Design for Communications Applications, Wiley, NY, 1996, Table A.1.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 111
Hua Loo Keng, Introduction To Number Theory, 'Table of least primitive roots for primes less than 50000', pp. 52-6, Springer NY 1982.
R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
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].
Anonymous, Primes less than 10000 and their smallest primitive roots
K. Matthews, Finding the least primitive root (mod p), p an odd prime
T. Oliveira e Silva, Least primitive root of prime numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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modulo 7: 3^6=1, 3^2=2, 3^7=3, 3^4=4, 3^5=5, 3^3=6, 7=p(4), 3=a(4)
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MAPLE
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with(numtheory); A001918 := primroot;
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MATHEMATICA
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(* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) Table[ PrimitiveRoot@Prime@n, {n, 101}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 15 2005)
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PROGRAM
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(PARI) for(x=1, 1000, print(lift(znprimroot(prime(x)))))
(Other) sage: print [primitive_root(p) for p in primes(570)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
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CROSSREFS
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A column of A060749. Cf. A002233.
Adjacent sequences: A001915 A001916 A001917 this_sequence A001919 A001920 A001921
Sequence in context: A127808 A127809 A127810 this_sequence A002233 A159953 A074595
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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