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

0,1

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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A084656 A073749 A299590 * A201866 A191632 A146918

Adjacent sequences: A250393 A250394 A250395 * A250397 A250398 A250399

Keyword

nonn

Author

Morgan L. Owens, Nov 21 2014

Status

approved