A250396 a(n) is the smallest prime greater than 2^n such that 2 is a primitive root modulo a(n).

3, 3, 5, 11, 19, 37, 67, 131, 269, 523, 1061, 2053, 4099, 8219, 16421, 32771, 65539, 131213, 262147, 524309, 1048589, 2097211, 4194371, 8388619, 16777259, 33554467, 67108933, 134217773, 268435459, 536871019, 1073741827, 2147483659, 4294967357, 8589934621, 17179869269, 34359738421, 68719476851, 137438953741

Offset: 0

Author

Morgan L. Owens, Nov 21 2014

Keywords

• nonn

References

• Henri Cohen, A Course in Computational Algebraic Number Theory, Springer Verlag, (1993)

Links

• Amiram Eldar, Table of n, a(n) for n = 0..300
• Joerg Arndt, Matters Computational; Ideas, Algorithms, Source Code, (§1.5.1, p.13).

Crossrefs

Cf. A104080 (smallest prime >= 2^n).

Programs

Mathematica

With[{n = 20},
Module[{p = NextPrime[2^n]},
  While[FreeQ[PrimitiveRootList[p], 2], p = NextPrime[p]]; p]]

PARI

a(n)=forprime(p=2^n+1,,if(znorder(Mod(2,p))==p-1,return(p))); \\ Joerg Arndt, Nov 21 2014