A081888 Numbers n such that the least positive primitive root of n is larger than the value for all positive numbers smaller than n.

1, 3, 4, 6, 22, 118, 191, 362, 842, 2042, 2342, 3622, 16022, 29642, 66602, 110881, 143522, 535802, 5070662, 6252122, 6497402, 10219442, 69069002, 1130187962

Offset

1,2

Comments

A081889 gives the primitive roots itself. Difference from A002229, A002230: In consideration of all n having primitive roots. A002229, A002230 only primes.

Links

Table of n, a(n) for n=1..24.

Formula

Numbers 1, 2, 4, p^m and 2*p^m have primitive roots for odd primes p and m >=1 natural number.

Maple

a306252 := proc(n::integer)
    local r;
    r := numtheory[primroot](n) ;
    if r <> FAIL then
        return r ;
    else
        return -1 ;
    end if;
end proc:
A081888 := proc()
    local rec, n, lpr ;
    rec := -1 ;
    for n from 1 do
        lpr := a306252(n) ;
        if lpr > rec then
            printf("%d, \n", n) ;
            rec := lpr ;
        end if;
    end do:
end proc:
A081888() ; # R. J. Mathar, Apr 04 2019

Mathematica

nmax = 10^5;
r[n_] := r[n] = Module[{prl = PrimitiveRootList[n]}, If[prl == {}, -1, prl[[1]]]]; r[1] = 1;
Reap[Module[{rec = -1, n, lpr}, For[n = 1, n <= nmax, n++, lpr = r[n]; If[lpr > rec, Print[n, " ", lpr]; Sow[n]; rec = lpr]]]][[2, 1]] (* Jean-François Alcover, Jun 19 2023, after R. J. Mathar *)

Prog

(Python)
from sympy import primitive_root
from itertools import count, islice
def f(n): r = primitive_root(n); return r if r != None else 0
def agen(r=0): yield from ((m, r:=f(m))[0] for m in count(1) if f(m) > r)
print(list(islice(agen(), 18))) # Michael S. Branicky, Feb 13 2023

Crossrefs

Cf. A081889, A002229, A002230. Positions of records of A306252.

Sequence in context: A265735 A038520 A294990 * A306493 A019209 A019120

Adjacent sequences: A081885 A081886 A081887 * A081889 A081890 A081891

Keyword

nonn,more

Author

Sven Simon, Mar 30 2003

Extensions

a(24) from Michael S. Branicky, Feb 20 2023

Status

approved