%I
%S 2,2,2,3,3,5,3,5,7,3,3,3,5,3,5,7,3,5,3,3,3,5,13,3,3,3,5,3,5,7,5,13,3,
%T 3,13,3,11,5,3,3,3,11,3,11,3,3,5,3,7,3,3,5,3,5,11,3,3,5,11,3,7,5,5,3,
%U 5,3,5,3,3,3,5,3,3,3,19,3,3,3,7,7,3,3,11,5,3,3,5,3,11,5,3,7
%N a(n) is the smallest b such that b^((p1)/2) == 1 (mod p) where p = A080076(n) is the nth Proth prime.
%C Proth's theorem asserts that p=1+k*2^m (with odd k < 2^m) is prime if there exists b such that b^((p1)/2) == 1 (mod n). This sequence lists the smallest b which certifies primality of A080076(n) via this relation.
%C For n > 3, a(n) is an odd prime.  _Thomas Ordowski_, Apr 23 2019
%F a(n) = A020649(A080076(n)) = A053760(k), where prime(k) = A080076(n).  _Thomas Ordowski_, Apr 23 2019
%o (PARI) A248972(n)=my(N=A080076[n]);for(a=0,9e9,Mod(a,N)^(N\2)==1&&return(a))
%o A080076=[];forprime(p=1,99999,isproth(p)&&(A080076=concat(A080076,p))&&print1(A248972(#A080076)","))
%o isproth(x)={ !bittest(x, 0) & (x>>valuation(x, 2))^2 < x }
%Y Cf. A080076.
%Y A subsequence of A020649 and of A053760.
%K nonn
%O 1,1
%A _M. F. Hasler_, Oct 18 2014
