A001918 - OEIS

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A001918

Least positive primitive root of n-th prime.
(Formerly M0242 N0083)

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; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

If k is a primitive root of p=4m+1, then p-k is too. If k is a primitive root of p=4m+3, then p-k isn't, but has order 2m+1. - Jon Perry, Sep 07 2014

REFERENCES

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.

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).

LINKS

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].

Loo-keng Hua, On the least primitive root of a prime, Bull. Amer. Math. Soc. 48 (1942), 726-730.

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, Primitive Root.

EXAMPLE

modulo 7: 3^6=1, 3^2=2, 3^7=3, 3^4=4, 3^5=5, 3^3=6, 7=prime(4), 3=a(4).

MAPLE

A001918 := proc(n)

numtheory[primroot](ithprime(n)) ;

end proc:

MATHEMATICA

Table[PrimitiveRoot@Prime@n, {n, 101}] (* Robert G. Wilson v, Dec 15 2005 *)