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A081888
Numbers n such that the least positive primitive root of n is larger than the value for all positive numbers smaller than n.
3
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.
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
KEYWORD
nonn,more
AUTHOR
Sven Simon, Mar 30 2003
EXTENSIONS
a(24) from Michael S. Branicky, Feb 20 2023
STATUS
approved