A047935 Consider primes p with least positive primitive root g such that q=p+g is next prime after p; sequence gives values of g.

1, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 6, 10, 2, 6, 2, 2, 2, 6, 2, 2, 6, 6, 2, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 2, 6, 2, 6, 6, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 10, 2, 2, 2, 2, 6, 2, 6, 2, 2, 2, 2, 6, 2, 2, 2, 2, 10, 6, 10, 2, 2, 2, 10, 2, 2, 2, 6, 10

Offset: 1

Author

Felice Russo

Keywords

• nice
• nonn

Examples

			11 has primitive root 2 and 11+2 = 13 is prime after 11, which contributes a 2 to the 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

Crossrefs

Cf. A047933, A047934. See also A001918.

Programs

Mathematica

f[p_] := {g = PrimitiveRoot[p], p + g == NextPrime[p]};
A047935 = Select[f /@ Prime /@ Range[1000], #[[2]]& ][[All, 1]](* Jean-François Alcover, Feb 15 2012 *)

Extensions

More terms from James Sellers, Dec 22 1999