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A070846
Smallest prime == 1 (mod 2n).
14
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
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, ", "))
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 15 2002
EXTENSIONS
More terms from Benoit Cloitre, May 18 2002
STATUS
approved