A071894 Largest positive primitive root (

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

Author

N. J. A. Sloane, Jun 11 2002

Keywords

• nonn
• easy

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].

Crossrefs

A diagonal of triangle in A060749.

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

Programs

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}]

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

Formula

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

Extensions

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