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
Keywords
Examples
a(4) = 5 since 5 = 2 + 3 < 7 is a primitive root mod prime(4) = 7 but 2 is not.
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.
Programs
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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}]
Comments