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A245014 Least prime p such that 2n*4^n divides p + 4n^2 + 1.

%I A245014 #46 Nov 14 2014 18:21:35
%S A245014 3,47,347,6079,10139,147311,687931,18874111,37748411,104857199,
%T A245014 276823579,805305791,29662117211,30064770287,64424508539,
%U A245014 2473901161471,11098195491707,7421703486191,83562883709531,527765581330879,369435906930971,27866022694353007,19421773393033147
%N A245014 Least prime p such that 2n*4^n divides p + 4n^2 + 1.
%C A245014 All those terms such that 2n*4^n is equal to p + 4n^2 + 1 belong to A247024.
%H A245014 Charles R Greathouse IV, <a href="/A245014/b245014.txt">Table of n, a(n) for n = 1..500</a>
%F A245014 a(n) << n^5*1024^n by Xylouris' version of Linnik's theorem. - _Charles R Greathouse IV_, Sep 18 2014
%t A245014 a[n_] := With[{k = n*2^(2*n+1)}, p = -4*n^2-1; While[!PrimeQ[p += k]]; p]; Table[a[n], {n, 1, 23}] (* _Jean-François Alcover_, Oct 09 2014, translated from _Charles R Greathouse IV_'s PARI code *)
%o A245014 (PARI) search(u)={ /* Slow, u must be a small integer. */
%o A245014   my(log2=log(2),q,t,t0,L1=List());
%o A245014   forprime(y=3,prime(10^u),
%o A245014     t=log(y+1)\log2;
%o A245014     while(t>t0,
%o A245014       q=4*t^2+y+1;
%o A245014       if(q%(t*(2^(2*t+1)))==0,
%o A245014         listput(L1,[t,y]);
%o A245014         t0=t;
%o A245014         break
%o A245014       ,
%o A245014         t--
%o A245014       )));
%o A245014   L1
%o A245014 }
%o A245014 (PARI) a(n)=my(k=n<<(2*n+1),p=-4*n^2-1); while(!isprime(p+=k),); p \\ _Charles R Greathouse IV_, Sep 18 2014
%Y A245014 Cf. A247024.
%K A245014 nonn
%O A245014 1,1
%A A245014 _R. J. Cano_ Sep 17 2014
%E A245014 a(10)-a(23) from _Charles R Greathouse IV_, Sep 18 2014