A047934 Consider primes p with least positive primitive root g such that q=p+g is next prime after p; sequence gives values of p.
2, 3, 5, 11, 29, 59, 101, 107, 149, 151, 179, 197, 227, 251, 269, 271, 337, 347, 367, 419, 461, 659, 733, 821, 827, 971, 991, 1019, 1021, 1061, 1091, 1229, 1277, 1301, 1427, 1451, 1619, 1667, 1787, 1877, 1931, 1949, 1997, 2027, 2141, 2237, 2267, 2309
Offset: 1
Examples
11 has primitive root 2 and 11+2 = 13 is prime after 11, so 11 is in sequence.
References
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
Links
- T. D. Noe, Table of n, a(n) for n=1..1000
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
- Index entries for primes by primitive root
Programs
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Mathematica
ok[p_] := (p + PrimitiveRoot[p] == NextPrime[p]); Select[Prime[Range[343]], ok] (* Jean-François Alcover, May 03 2011 *) Transpose[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]] == PrimitiveRoot[ #[[1]]]&]][[1]] (* Harvey P. Dale, Oct 08 2012 *)
Extensions
More terms from James Sellers, Dec 22 1999