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 A243403 Number of primes p < n such that p*(n-p) is a primitive root modulo prime(n). 5
 0, 0, 1, 1, 2, 0, 3, 2, 3, 2, 1, 3, 3, 2, 3, 4, 4, 1, 4, 1, 2, 2, 5, 8, 5, 1, 1, 5, 3, 6, 6, 7, 6, 6, 4, 2, 4, 3, 6, 11, 6, 4, 3, 7, 6, 8, 3, 2, 10, 9, 6, 11, 2, 8, 9, 9, 5, 2, 5, 2, 3, 13, 5, 14, 8, 12, 7, 8, 9, 6, 13, 9, 4, 10, 3, 13, 12, 4, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Conjecture: a(n) > 0 for all n > 6. We have verified this for all n = 7, ..., 2*10^5. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, New observations on primitive roots modulo primes, arXiv:1405.0290 [math.NT], 2014. EXAMPLE a(18) = 1 since 17 is prime with 17*(18-17) = 17 a primitive root modulo prime(18) = 61. a(20) = 1 since 11 is prime with 11*(20-11) = 99 a primitive root modulo prime(20) = 71. a(26) = 1 since 2 is prime with 2*(26-2) = 48 a primitive root modulo prime(26) = 101. a(27) = 1 since 17 is prime with 17*(27-17) = 170 a primitive root modulo prime(27) = 103. MATHEMATICA dv[n_]:=Divisors[n] Do[m=0; Do[Do[If[Mod[(Prime[k]*(n-Prime[k]))^(Part[dv[Prime[n]-1], i]), Prime[n]]==1, Goto[aa]], {i, 1, Length[dv[Prime[n]-1]]-1}]; m=m+1; Label[aa]; Continue, {k, 1, PrimePi[n-1]}]; Print[n, " ", m]; Continue, {n, 1, 80}] CROSSREFS Cf. A000040, A000720, A243164. Sequence in context: A324397 A132623 A277890 * A051613 A173291 A341889 Adjacent sequences:  A243400 A243401 A243402 * A243404 A243405 A243406 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jun 04 2014 STATUS approved

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Last modified May 25 10:05 EDT 2022. Contains 354066 sequences. (Running on oeis4.)