A245014 - OEIS

%I #46 Nov 14 2014 18:21:35

%S 3,47,347,6079,10139,147311,687931,18874111,37748411,104857199,

%T 276823579,805305791,29662117211,30064770287,64424508539,

%U 2473901161471,11098195491707,7421703486191,83562883709531,527765581330879,369435906930971,27866022694353007,19421773393033147

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

%C All those terms such that 2n*4^n is equal to p + 4n^2 + 1 belong to A247024.

%H Charles R Greathouse IV, <a href="/A245014/b245014.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) << n^5*1024^n by Xylouris' version of Linnik's theorem. - _Charles R Greathouse IV_, Sep 18 2014

%t 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 (PARI) search(u)={ /* Slow, u must be a small integer. */

%o   my(log2=log(2),q,t,t0,L1=List());

%o   forprime(y=3,prime(10^u),

%o     t=log(y+1)\log2;

%o     while(t>t0,

%o       q=4*t^2+y+1;

%o       if(q%(t*(2^(2*t+1)))==0,

%o         listput(L1,[t,y]);

%o         t0=t;

%o         break

%o       ,

%o         t--

%o       )));

%o   L1

%o }

%o (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 Cf. A247024.

%K nonn

%O 1,1

%A _R. J. Cano_ Sep 17 2014

%E a(10)-a(23) from _Charles R Greathouse IV_, Sep 18 2014