A249382 - OEIS

%I #12 Nov 21 2014 21:28:12

%S 3,3,7,3,3,31,7,61,13,7,43,31,19,3,31,307,733,79,43,73,421,73,181,19,

%T 157,181,3,739,421,127,103,73,571,421,109,211,1459,103,1693,487,829,

%U 139,1153,439,3067,601,199,853,421,3541,1069,1279,1297

%N Smallest odd prime Q such that Q*2^prime(n)-1 is also a prime number.

%H Pierre CAMI, <a href="/A249382/b249382.txt">Table of n, a(n) for n = 1..1800</a>

%e 3*2^2-1=11 prime so a(1)=3 as 2 is prime(1).

%e 3*2^3-1=23 prime so a(2)=3 as 3 is prime(2).

%e 3*2^5-1=95 composite.

%e 5*2^5-1=159 composite.

%e 7*2^5-1=223 prime so a(3)=7 as 5 is prime(3).

%t a249382[n_Integer] := Module[{q = 2}, While[! PrimeQ[Prime[q]*2^Prime[n] - 1], q++]; Prime[q]]; a249382/@Range[53] (* _Michael De Vlieger_, Nov 12 2014 *)

%o (PFGW & SCRIPT)

%o SCRIPT

%o DIM i

%o DIM j

%o DIM n,0

%o OPENFILEOUT myf,a(n)

%o LABEL loop1

%o SET n,n+1

%o SET i,1

%o LABEL loop2

%o SET i,i+1

%o SET j,p(i)

%o PRP j*2^p(n)-1

%o IF ISPRP THEN GOTO a

%o GOTO loop2

%o LABEL a

%o WRITE myf,j

%o GOTO loop1

%o (PARI) listp(nn) = {for (n=1, nn, k=2; while(!isprime(prime(k)*2^prime(n)-1), k++); print1(prime(k), ", "););} \\ _Michel Marcus_, Oct 27 2014

%Y Cf. A249383, A249384.

%K nonn

%O 1,1

%A _Pierre CAMI_, Oct 27 2014