A070846 Smallest prime == 1 (mod 2n).

3, 5, 7, 17, 11, 13, 29, 17, 19, 41, 23, 73, 53, 29, 31, 97, 103, 37, 191, 41, 43, 89, 47, 97, 101, 53, 109, 113, 59, 61, 311, 193, 67, 137, 71, 73, 149, 229, 79, 241, 83, 337, 173, 89, 181, 277, 283, 97, 197, 101, 103, 313, 107, 109, 331, 113, 229, 233, 709, 241

Offset

1,1

Comments

From Jianing Song, Feb 14 2021: (Start)

a(n) is the smallest prime p such that there is a primitive 2n-th root of unity modulo p, i.e., there is an element with order 2n in the multiplicative group of integers modulo p.

For n > 1, a(n) is the smallest prime p such that the 2n-th cyclotomic field Q(exp(2*Pi*i/(2*n))) can be embedded into the p-adic field Q_p. (End)

Links

Dmitry Kamenetsky, Table of n, a(n) for n = 1..50000

Formula

a(n) = 2*n*A016014(n) + 1. - Dmitry Kamenetsky, Oct 26 2016

Mathematica

With[{prs=Prime[Range[200]]}, Flatten[Table[Select[prs, Mod[#, 2n]==1&, 1], {n, 60}]]] (* Harvey P. Dale, Jan 16 2013 *)

Prog

(PARI) for(n=1, 80, s=1; while((isprime(s)*s-1)%(2*n)>0, s++); print1(s, ", "))

Crossrefs

Cf. A070847, A070848, A070849, A070850, A070851, A070852, A070853.

Cf. A034694, A016014.

Sequence in context: A291107 A132445 A307437 * A078683 A099863 A112092

Adjacent sequences: A070843 A070844 A070845 * A070847 A070848 A070849

Keyword

nonn

Author

Amarnath Murthy, May 15 2002

Extensions

More terms from Benoit Cloitre, May 18 2002

Status

approved