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A242277
Least positive primitive root g < prime(n) mod prime(n) such that g is the sum of the first k primes for some k > 0, or 0 if such a number g does not exist.
2
0, 2, 2, 5, 2, 2, 5, 2, 5, 2, 17, 2, 17, 5, 5, 2, 2, 2, 2, 28, 5, 28, 2, 28, 5, 2, 5, 2, 10, 5, 58, 2, 5, 2, 2, 77, 5, 2, 5, 2, 2, 2, 28, 5, 2, 41, 2, 5, 2, 10, 5, 41, 129, 77, 5, 5, 2, 58, 5, 41, 5, 2, 5, 17, 10, 2, 28, 10, 2, 2, 5, 28, 10, 2, 2, 5, 2, 5, 17, 28
OFFSET
1,2
COMMENTS
According to the conjecture in A242266, a(n) should be positive for all n > 1.
LINKS
Zhi-Wei Sun, Notes on primitive roots modulo primes, arXiv:1405.0290 [math.NT], 2014.
EXAMPLE
a(4) = 5 since 5 = 2 + 3 < 7 is a primitive root mod prime(4) = 7 but 2 is not.
MATHEMATICA
f[0]=0
f[n_]:=Prime[n]+f[n-1]
dv[n_]:=Divisors[n]
Do[Do[If[f[k]>=Prime[n], Goto[cc]]; Do[If[Mod[f[k]^(Part[dv[Prime[n]-1], i]), Prime[n]]==1, Goto[aa]], {i, 1, Length[dv[Prime[n]-1]]-1}]; Print[n, " ", f[k]]; Goto[bb]; Label[aa]; Continue, {k, 1, n}]; Label[cc]; Print[n, " ", 0]; Label[bb]; Continue, {n, 1, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 10 2014
STATUS
approved