A138291 Number of primes of the form prime(n)+g, where g is a primitive root of prime(n).

1, 1, 1, 0, 3, 1, 3, 1, 2, 4, 2, 2, 4, 3, 2, 7, 10, 3, 3, 3, 4, 6, 10, 7, 6, 11, 7, 12, 7, 9, 6, 10, 14, 10, 17, 10, 10, 12, 11, 13, 22, 7, 9, 11, 16, 10, 5, 13, 23, 8, 23, 12, 9, 23, 26, 22, 25, 13, 12, 14, 13, 19, 12, 18, 14, 32, 17, 18, 30, 22, 32, 21, 20, 14, 17, 28, 30, 19, 19, 21

Offset: 1

Author

T. D. Noe, Mar 12 2008

Keywords

• nonn

Comments

It appears that only a(4), corresponding to the prime 7, is zero.

Examples

			a(5)=3 because the primitive roots of 11 are 2, 6, 7 and 8. Adding these numbers to 11 produce three primes: 13, 17 and 19.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..2000
• Eric Weisstein, MathWorld: Primitive Root

Crossrefs

Cf. A047934, A060749 (triangle of primitive roots of primes).

Programs

Mathematica

Join[{1}, Table[p=Prime[n]; g=Select[Range[2,p-1], MultiplicativeOrder[ #,p]==p-1&]; Length[Select[p+g, PrimeQ]], {n,2,2000}]]
Table[Count[p+PrimitiveRootList[p],?PrimeQ],{p,Prime[Range[80]]}] (* _Harvey P. Dale, Aug 03 2021 *)