login
A071894
Largest positive primitive root (<p) of n-th prime p.
10
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 11, 2002
EXTENSIONS
More terms from Robert G. Wilson v, Jun 11 2002
STATUS
approved