A224489 - OEIS

%I #27 Sep 08 2022 08:46:04

%S 1,1,3,1,1,1,1,4,4,6,4,6,1,1,9,10,1,6,4,7,1,4,3,4,3,10,4,4,1,1,1,10,1,

%T 7,6,12,1,9,6,3,1,1,6,3,1,1,1,3,3,4,4,21,4,1,3,1,6,4,1,10,3,1,15,1,3,

%U 4,9,13,10,9,1,4,1,3,1,3,12,9,6,1,1,22,4,1

%N Smallest k such that k*2*p(n)^2-1 is prime.

%H Pierre CAMI, <a href="/A224489/b224489.txt">Table of n, a(n) for n = 1..10000</a>

%e 1*2*2^2-1=7 is prime, p(1)=2 so a(1)=1.

%e 1*2*3^2-1=17 is prime, p(2)=3 so a(2)=1.

%e 1*2*5^2-1=49 is composite; 2*2*5^2-1=99 is composite; 3*2*5^2-1=149 is prime, p(3)=5 so a(3)=3.

%t a[n_] := For[k = 1, True, k++, If[ PrimeQ[k*2*Prime[n]^2 - 1], Return[k]]]; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Apr 10 2013 *)

%o PFGW and SCRIPTIFY

%o SCRIPT

%o DIM k

%o DIM i,0

%o DIM q

%o DIMS t

%o OPENFILEOUT myf,a(n).txt

%o LABEL a

%o SET i,i+1

%o IF i>50000 THEN END

%o SET k,0

%o LABEL b

%o SET k,k+1

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

%o SET q,k*2*p(i)^2-1

%o PRP q,t

%o IF ISPRP THEN WRITE myf,t

%o IF ISPRP THEN GOTO a

%o GOTO b

%o (Magma)

%o S:=[];

%o k:=1;

%o for n in [1..90] do

%o   while not IsPrime(k*2*NthPrime(n)^2-1) do

%o        k:=k+1;

%o   end while;

%o   Append(~S, k);

%o   k:=1;

%o end for;

%o S; // _Bruno Berselli_, Apr 18 2013

%Y Cf. A224490, A224491, A224492.

%K nonn

%O 1,3

%A _Pierre CAMI_, Apr 08 2013