A128906 Difference between the greatest primitive root and the least primitive root of the n-th prime.

0, 0, 1, 2, 6, 9, 11, 13, 16, 25, 21, 33, 29, 31, 40, 49, 54, 57, 61, 62, 63, 74, 78, 83, 87, 97, 96, 102, 97, 107, 115, 126, 131, 133, 145, 140, 147, 157, 160, 169, 174, 177, 170, 183, 193, 194, 205, 211, 222, 217, 227, 230, 227, 242, 251, 256, 265, 263, 267, 275, 274

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..1001 (adapted to offset 1 by Sidney Cadot).

Formula

a(n) = A071894(n) - A001918(n).

Mathematica

Table[(k=p-1; While[MultiplicativeOrder[k, p]!=p-1, k--]; k)-PrimitiveRoot@p, {p, Prime@Range@100}] (* Giorgos Kalogeropoulos, Sep 28 2023 *)

Prog

(PARI) a(n)=my(p=prime(n)); forstep(r=p-1, 2, -1, if(znorder(Mod(r, p))==p-1, return(r-lift(znprimroot(p)))));
vector(66, n, a(n)) \\ Joerg Arndt, Sep 29 2023

Crossrefs

Cf. A001918, A071894.

Sequence in context: A066586 A146974 A133160 * A192420 A139639 A187690

Adjacent sequences: A128903 A128904 A128905 * A128907 A128908 A128909

Keyword

nonn

Author

Robert G. Wilson v, Apr 21 2007

Extensions

a(1)=0 inserted by Georg Fischer, Dec 11 2022

Status

approved