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A023048
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Smallest prime having least positive primitive root n, or 0 if no such prime exists.
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6
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2, 3, 7, 0, 23, 41, 71, 0, 0, 313, 643, 4111, 457, 1031, 439, 0, 311, 53173, 191, 107227, 409, 3361, 2161, 533821, 0, 12391, 0, 133321, 15791, 124153, 5881, 0, 268969, 48889, 64609, 0, 36721, 55441, 166031, 1373989, 156601, 2494381, 95471, 71761, 95525767
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = 0 iff n is a prime power p^k, k >= 2 (i.e. a member of A001592).
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REFERENCES
| A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XLIV.
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n=1..107 (from the web page of Tomas Oliveira e Silva)
Wouter Meeussen, Smallest Primes with Specified Least Primitive Root
Tomas Oliveira e Silva, Least primitive root of prime numbers
Index entries for primes by primitive root
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EXAMPLE
| a(2) = 3, since 3 has 2 as smallest positive primitive root and no prime p < 3 has 2 as smallest positive primitive root. a(24) = 533821, since prime 533821 has 24 as smallest positive primitive root and no prime p < 533821 has 24 as smallest positive primitive root.
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MATHEMATICA
| (* first load package *) << NumberTheory`NumberTheoryFunctions` (* then do *) t = Table[0, {100}]; Do[a = PrimitiveRoot@Prime@n; If[a < 101 && t[[a]] == 0, t[[a]] = n], {n, 10^6}]; Unprotect[Prime]; Prime[0] = 0; Prime@t; Clear[Prime]; Protect[Prime] (from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 15 2005)
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CROSSREFS
| Cf. A001122-A001126, A061323-A061335, A061730-A061741. Index of primes: A066529.
For records see A133433. See A133432 for a version without the 0's.
Sequence in context: A201363 A117024 A203143 * A083521 A104691 A011160
Adjacent sequences: A023045 A023046 A023047 * A023049 A023050 A023051
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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