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

Author

Amarnath Murthy, May 15 2002

Keywords

• nonn

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

Crossrefs

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

Cf. A034694, A016014.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

More terms from Benoit Cloitre, May 18 2002