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Supersequence of A047936 = primes whose smallest positive primitive root is not prime. (Proof. If p is not in A222717, then the smallest positive quadratic nonresidue of p is a primitive root g. Since the smallest positive quadratic nonresidue is always a prime, g is prime. But since all primitive roots are quadratic nonresidues, g is the smallest positive primitive root of p. Hence p is not in A047936.)
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2, 41, 43, 103, 109, 151, 157, 191, 229, 251, 271, 277, 283, 307, 311, 313, 331, 337, 367, 397, 409, 439, 457, 499, 571, 643, 683, 691, 727, 733, 739, 761, 769, 811, 911, 919, 967, 971, 991, 997, 1013, 1021, 1031, 1051, 1069, 1093, 1151, 1163, 1181, 1289, 1297
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2, 41, 43, 103, 109, 151, 157, 191, 229, 251, 271, 277, 283, 307, 311, 313, 331, 337, 367, 397, 409, 439, 457, 499, 571, 643, 683, 691, 727, 733, 739, 761, 769, 811, 911, 919, 967, 971, 991, 997, 1013, 1021, 1031, 1051, 1069, 1093, 1151, 1163, 1181, 1289, 1297, 1303, 1321, 1399, 1429, 1459, 1471, 1489, 1543, 1559, 1579, 1597, 1613, 1627, 1657, 1699, 1709, 1723, 1753, 1759, 1783, 1789, 1811, 1871, 1873, 1879, 1933
nn = 300; NR = (Table[p = Prime[n]; First[ Select[ Range[p], JacobiSymbol[#, p] != 1 &]], {n, 1, 300nn}]); Select[ Prime[ Range[300nn]], Mod[ NR[[PrimePi[#]]], #] == 0 || MultiplicativeOrder[ NR[[PrimePi[#]]], #] < # - 1 &]
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