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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A001918 A268616 A002233 * A273458 A159953 A074595

Adjacent sequences:  A241513 A241514 A241515 * A241517 A241518 A241519

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Apr 24 2014

STATUS

approved

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Last modified January 17 16:11 EST 2019. Contains 319235 sequences. (Running on oeis4.)