%I #24 Dec 16 2023 14:07:33

%S 3,5,7,17,11,13,29,17,19,41,23,73,53,29,31,97,103,37,191,41,43,89,47,

%T 97,101,53,109,113,59,61,311,193,67,137,71,73,149,229,79,241,83,337,

%U 173,89,181,277,283,97,197,101,103,313,107,109,331,113,229,233,709,241

%N Smallest prime == 1 (mod 2n).

%C From _Jianing Song_, Feb 14 2021: (Start)

%C 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.

%C 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)

%H Dmitry Kamenetsky, <a href="/A070846/b070846.txt">Table of n, a(n) for n = 1..50000</a>

%F a(n) = 2*n*A016014(n) + 1. - _Dmitry Kamenetsky_, Oct 26 2016

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

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

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

%Y Cf. A034694, A016014.

%K nonn

%O 1,1

%A _Amarnath Murthy_, May 15 2002

%E More terms from _Benoit Cloitre_, May 18 2002