A241516 Least positive primitive root g < prime(n) modulo prime(n) which is also a partition number given by A000041, or 0 if such a number g does not exist.

1, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 7, 3, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 5, 2, 11, 3, 3, 2, 3, 2, 2, 7, 5, 2, 5, 2, 2, 2, 22, 5, 2, 3, 2, 3, 2, 7, 3, 7, 7, 11, 3, 5, 2, 15, 5, 3, 3, 2, 5, 22, 15, 2, 3, 15, 2, 2, 3, 7, 11, 2, 2, 5, 2, 5, 3, 22

Offset

1,2

Comments

According to the conjecture in A241504, a(n) should be always positive.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014.

Example

a(4) = 3 since 3 = A000041(3) is a primitive root modulo prime(4) = 7, but neither 1 = A000041(1) nor 2 = A000041(2) is.

Mathematica

f[k_]:=PartitionsP[k]
dv[n_]:=Divisors[n]
Do[Do[If[f[k]>Prime[n]-1, 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, " ", PartitionsP[k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Prime[n]-1}]; Label[cc]; Print[Prime[n], " ", 0]; Label[bb]; Continue, {n, 1, 80}]

Crossrefs

Cf. A000040, A000041, A237121, A239957, A239963, A241476, A241492, A241504.

Sequence in context: A268616 A331506 A002233 * A273458 A159953 A074595

Adjacent sequences: A241513 A241514 A241515 * A241517 A241518 A241519

Keyword

nonn

Author

Zhi-Wei Sun, Apr 24 2014

Status

approved