A127807 Least positive primitive root of (n-th prime)^2.

3, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 6, 3, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 5, 2, 6, 3, 3, 2, 3, 2, 2, 6, 5, 2, 5, 2, 2, 2, 19, 5, 2, 3, 2, 3, 2, 6, 3, 7, 7, 6, 3, 5, 2, 6, 5, 3, 3, 2, 5, 17, 10, 2, 3, 10, 2, 2, 3, 7, 6, 2, 2, 5, 2, 5, 3, 21, 2, 2, 7, 5, 15, 2, 3, 13, 2, 3, 2, 13, 3, 2, 7, 5, 2, 3, 2, 2

Offset: 1

Author

Artur Jasinski, Jan 29 2007

Keywords

• nonn
• easy

Comments

A055578 lists the indices n such that a(n) differs from A001918(n).

References

• D. Cohen, R. W. K. Odoni, and W. W. Stothers, On the Least Primitive Root Modulo p^2, Bulletin of the London Mathematical Society 6:1 (March 1974), pp. 42-46.

Links

• Bryce Kerr, Kevin McGown, and Tim Trudgian, The least primitive root modulo p^2. arXiv:1908.11497 [math.NT]

Crossrefs

Cf. A001918, A127808, A127809, A127810.

Programs

Mathematica

<< NumberTheory`NumberTheoryFunctions` Table[PrimitiveRoot[(Prime[n])^2], {n, 1, 100}]
PrimitiveRoot[Prime[Range[100]]^2] (* Harvey P. Dale, Aug 19 2017 *)

Formula

Cohen, Odoni, & Stothers prove that a(n) < prime(n)^(1/4 + e) for any e > 0 and all large enough n. Kerr, McGown, & Trudgian give an effective version: a(n) < prime(n)^0.99 for all n. - Charles R Greathouse IV, Apr 28 2020