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.

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, 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: A021448 A359246 A229709 * A241476 A309727 A195719

Adjacent sequences: A242274 A242275 A242276 * A242278 A242279 A242280

Keyword

nonn

Author

Zhi-Wei Sun, May 10 2014

Status

approved