A071894 Largest positive primitive root (<p) of n-th prime p.

1, 2, 3, 5, 8, 11, 14, 15, 21, 27, 24, 35, 35, 34, 45, 51, 56, 59, 63, 69, 68, 77, 80, 86, 92, 99, 101, 104, 103, 110, 118, 128, 134, 135, 147, 146, 152, 159, 165, 171, 176, 179, 189, 188, 195, 197, 207, 214, 224, 223, 230, 237, 234, 248, 254, 261, 267, 269, 272

Offset

1,2

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.

R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.

Links

T. D. Noe, 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].

Formula

a(n) = prime(n) - A002199(n) - T. D. Noe, Oct 24 2005

Mathematica

f[n_] := Block[{k = Prime[n] - 1, p = Prime[n], t = Table[i, {i, 1, Prime[n] - 1}]}, While[ Union[ PowerMod[ k, t, p]] != t, k-- ]; k]; Table[ f[n], {n, 1, 60}]

Prog

(PARI) a(n) = my(p=prime(n)); forstep(q=p-1, 1, -1, if(znorder(Mod(q, p))==eulerphi(p), return(q))); \\ Michel Marcus, Sep 28 2023

Crossrefs

A diagonal of triangle in A060749.

Cf. A000040, A001918 (least positive primitive root), A002199.

Sequence in context: A171048 A209292 A185371 * A301892 A271876 A358533

Adjacent sequences: A071891 A071892 A071893 * A071895 A071896 A071897

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 11, 2002

Extensions

More terms from Robert G. Wilson v, Jun 11 2002

Status

approved