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 A179858 Least positive primitive root of A139035(n). 0
 3, 5, 5, 7, 3, 5, 5, 19, 3, 7, 5, 6, 17, 7, 6, 5, 3, 13, 3, 5, 7, 3, 5, 11, 5, 3, 3, 11, 5, 5, 5, 5, 6, 14, 3, 3, 3, 17, 5, 3, 3, 6, 13, 5, 7, 3, 5, 11, 5, 19, 3, 5, 5, 3, 6, 10, 5, 5, 14, 6, 3, 7, 5, 5, 7, 5, 3, 3, 11, 5, 5, 3, 5, 6, 7, 3, 5, 7, 3, 7, 5, 5, 5, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is a prime, then a is called a semiprimitive root if it has order (p-1)/2 and there is no x for which a^x is congruent to -1 (mod p). So +- a^k, 0 <= k <= (p-3)/2 is a complete set of nonzero residues (mod p). A primitive root has order p-1, so a number cannot be both a primitive root and a semiprimitive root. A139035(n) are the primes for which 2 is a semiprimitive root. This sequence gives the smallest positive primitive root corresponding to each member of A139035, so each member is greater than or equal to 3. LINKS EXAMPLE Since A139035(13)=311, 2 is a semiprimitive root of 311 so j=0,...,154, {+-2^j} is a complete set of residues (congruent to {1,...,310}).  The corresponding member of this sequence is a(13)=17 because 17 is the smallest positive integer a for which {a^k}, k=0,...,309 is a complete set of residues. MATHEMATICA PrimitiveRoot /@ Reap[For[p = 3, p < 3000, p = NextPrime[p], rp = MultiplicativeOrder[2, p]; rm = MultiplicativeOrder[-2, p]; If[rp != p-1 && rm == p-1, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Sep 03 2016, after Joerg Arndt's code for A139035 *) CROSSREFS Cf. A001918, A139035. Sequence in context: A197631 A266567 A282624 * A141501 A277776 A103988 Adjacent sequences:  A179855 A179856 A179857 * A179859 A179860 A179861 KEYWORD nonn AUTHOR Vladimir Shevelev, Jan 11 2011 EXTENSIONS More terms from Jean-François Alcover, Sep 03 2016 STATUS approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)