OFFSET
1,5
COMMENTS
Conjecture: a(n) > 0 for all n > 6.
We have verified this for all n = 7, ..., 2*10^5.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, New observations on primitive roots modulo primes, arXiv:1405.0290 [math.NT], 2014.
EXAMPLE
a(18) = 1 since 17 is prime with 17*(18-17) = 17 a primitive root modulo prime(18) = 61.
a(20) = 1 since 11 is prime with 11*(20-11) = 99 a primitive root modulo prime(20) = 71.
a(26) = 1 since 2 is prime with 2*(26-2) = 48 a primitive root modulo prime(26) = 101.
a(27) = 1 since 17 is prime with 17*(27-17) = 170 a primitive root modulo prime(27) = 103.
MATHEMATICA
dv[n_]:=Divisors[n]
Do[m=0; Do[Do[If[Mod[(Prime[k]*(n-Prime[k]))^(Part[dv[Prime[n]-1], i]), Prime[n]]==1, Goto[aa]], {i, 1, Length[dv[Prime[n]-1]]-1}]; m=m+1; Label[aa]; Continue, {k, 1, PrimePi[n-1]}];
Print[n, " ", m]; Continue, {n, 1, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jun 04 2014
STATUS
approved