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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS According to the conjecture in A242266, a(n) should be positive for all n > 1. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 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 Cf. A000040, A007504, A242266. Sequence in context: A319771 A021448 A229709 * A241476 A309727 A195719 Adjacent sequences:  A242274 A242275 A242276 * A242278 A242279 A242280 KEYWORD nonn AUTHOR Zhi-Wei Sun, May 10 2014 STATUS approved

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Last modified September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)