A248972 - OEIS

%I #34 Apr 29 2019 11:01:04

%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^((p-1)/2) == -1 (mod p) where p = A080076(n) is the n-th 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^((p-1)/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