A070846 - OEIS

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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

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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.