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

1,5

Comments

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

Links

T. D. Noe, Table of n, a(n) for n=1..2000

Eric Weisstein, MathWorld: Primitive Root

Example

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.

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 *)

Crossrefs

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

Sequence in context: A030728 A237712 A227920 * A201681 A062174 A154754

Adjacent sequences: A138288 A138289 A138290 * A138292 A138293 A138294

Keyword

nonn

Author

T. D. Noe, Mar 12 2008

Status

approved