A261388 a(n) is the length of the longest stretch of consecutive primitive roots of the multiplicative group modulo prime(n).

1, 1, 2, 1, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 4, 5, 5, 2, 3, 3, 3, 3, 7, 6, 5, 4, 5, 6, 4, 3, 4, 4, 5, 4, 6, 4, 4, 4, 6, 5, 6, 3, 5, 4, 5, 3, 4, 5, 7, 4, 7, 6, 4, 5, 6, 7, 9, 4, 4, 4, 9, 5, 4, 5, 4, 6, 4, 3, 8, 6, 7, 8, 5, 5, 4, 8, 5, 3, 5, 7, 8, 6, 6, 4, 4, 6, 9, 5, 4, 4, 11, 11, 5, 5, 5, 8, 7, 5, 6

Offset

1,3

Links

Joerg Arndt, Table of n, a(n) for n = 1..9592 (terms for all primes < 10^5)

Mathematica

a[n_] := 1 + Max[ Join[{0}, Length/@ Select[ Split@ Differences @ PrimitiveRootList @ Prime @ n, #[[1]] == 1 &]]]; Array[a, 99] (* Giovanni Resta, Aug 17 2015 *)

Prog

(PARI)
consec_pr(p)= \\ max number of consecutive primroots
{
    my( v = vector(p-1) );
    my (g = znprimroot(p) );
    for (j=1, p-1,  if (gcd(p-1, j)==1, v[lift(g^j)]=1 ) );
    my ( m=0, t=0 );
    for (j=1, p-1, if ( v[j]==0, t=0 , t+=1; if ( t>m, m=t ); ); );
    return(m);
}
forprime(p=2, 10^3, c=consec_pr(p);  print1( c, ", " ); );

Crossrefs

Cf. A261438 (primes corresponding to records).

Sequence in context: A219609 A087825 A263100 * A369793 A253281 A029206

Adjacent sequences: A261385 A261386 A261387 * A261389 A261390 A261391

Keyword

nonn

Author

Joerg Arndt, Aug 17 2015

Status

approved