A245601 - OEIS

%I #19 Feb 08 2015 16:45:56

%S 3,2,7,2,181,503,43,281,919,397,2099,389,163,89,5641,751,1951,353,2,

%T 3709,4673,1607,769,7699,107,7069,17,13147,7841,97,5741,2383,5557,251,

%U 9661,14969,269,2753,18451,2797,4729,29,15649,5387,8539,13001,1481,2

%N Smallest prime Q such that prime(n)*(2*Q)^prime(n)+1 is prime.

%H Pierre CAMI and Jens Kruse Andersen, <a href="/A245601/b245601.txt">Table of n, a(n) for n = 1..200</a> (first 100 terms from Pierre CAMI)

%e 2*(2*2)^2 + 1 = 33 composite.

%e 2*(2*3)^2 + 1 = 73 prime so a(1) = 3.

%t a245601[n_Integer] := Catch[

%t   Do[

%t    If[And[PrimeQ[Q], PrimeQ[Prime[n]*(2*Q)^Prime[n] + 1]] == True,

%t     Throw[Q]],

%t    {Q, 1000000}]

%t   ]; Map[a245601, Range[50]] (* _Michael De Vlieger_, Aug 03 2014 *)

%o (PFGW & SCRIPT)

%o SCRIPT

%o DIM i,0

%o DIM n

%o DIMS t

%o OPENFILEOUT myf,b(n).txt

%o LABEL loop1

%o SET i,i+1

%o IF i>100 THEN END

%o SET n,0

%o LABEL loop2

%o SET n,n+1

%o SETS t,%d,%d\,;p(i);p(n)

%o PRP p(i)*(2*p(n))^p(i)+1,t

%o IF ISPRP THEN GOTO a

%o GOTO loop2

%o LABEL a

%o WRITE myf,t

%o GOTO loop1

%o (PARI) a(n)=for(k=1,10^5,if(ispseudoprime(prime(n)*(2*prime(k))^prime(n)+1),return(prime(k))))

%o n=1;while(n<100,print1(a(n),", ");n++) \\ _Derek Orr_, Jul 27 2014

%Y Cf. A245597, A245598, A245600.

%K nonn

%O 1,1

%A _Pierre CAMI_, Jul 27 2014