OFFSET
1,1
COMMENTS
An alternative description: Numbers k such that 1/k in base 6 generates a repeating fraction with period phi(n) and n/2 < phi(n) < n-1.
For example, in base 6, 1/121 has repeat length 110 = phi(121) which is > 121/2 but less than 121-1.
LINKS
Robert Hutchins, PrimRoot.c
MAPLE
isA033948 := proc(n)
if n in {1, 2, 4} then
true;
elif type(n, 'odd') and nops(numtheory[factorset](n)) = 1 then
true;
elif type(n, 'even') and type(n/2, 'odd') and nops(numtheory[factorset](n/2)) = 1 then
true;
else
false;
end if;
end proc:
isA167794 := proc(n)
if not isA033948(n) or n = 1 then
false;
elif numtheory[order](6, n) = numtheory[phi](n) then
true;
else
false;
end if;
end proc:
A346316 := proc(n)
option remember;
local a;
if n = 1 then
121;
else
for a from procname(n-1)+1 do
if not isprime(a) and isA167794(a) then
return a;
end if;
end do:
end if;
end proc:
seq(A346316(n), n=1..20) ; # R. J. Mathar, Sep 15 2021
MATHEMATICA
Select[Range[160000], CompositeQ[#] && PrimitiveRoot[#, 6] == 6 &] (* Amiram Eldar, Jul 13 2021 *)
PROG
(PARI) isok(m) = (m>1) && !isprime(m) && (gcd(m, 6)==1) && (znorder(Mod(6, m))==eulerphi(m)); \\ Michel Marcus, Aug 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Hutchins, Jul 13 2021
STATUS
approved