cp's OEIS Frontend

A249382 Smallest odd prime Q such that Q*2^prime(n)-1 is also a prime number.

%I A249382 #12 Nov 21 2014 21:28:12
%S A249382 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 A249382 157,181,3,739,421,127,103,73,571,421,109,211,1459,103,1693,487,829,
%U A249382 139,1153,439,3067,601,199,853,421,3541,1069,1279,1297
%N A249382 Smallest odd prime Q such that Q*2^prime(n)-1 is also a prime number.
%H A249382 Pierre CAMI, <a href="/A249382/b249382.txt">Table of n, a(n) for n = 1..1800</a>
%e A249382 3*2^2-1=11 prime so a(1)=3 as 2 is prime(1).
%e A249382 3*2^3-1=23 prime so a(2)=3 as 3 is prime(2).
%e A249382 3*2^5-1=95 composite.
%e A249382 5*2^5-1=159 composite.
%e A249382 7*2^5-1=223 prime so a(3)=7 as 5 is prime(3).
%t A249382 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 A249382 (PFGW & SCRIPT)
%o A249382 SCRIPT
%o A249382 DIM i
%o A249382 DIM j
%o A249382 DIM n,0
%o A249382 OPENFILEOUT myf,a(n)
%o A249382 LABEL loop1
%o A249382 SET n,n+1
%o A249382 SET i,1
%o A249382 LABEL loop2
%o A249382 SET i,i+1
%o A249382 SET j,p(i)
%o A249382 PRP j*2^p(n)-1
%o A249382 IF ISPRP THEN GOTO a
%o A249382 GOTO loop2
%o A249382 LABEL a
%o A249382 WRITE myf,j
%o A249382 GOTO loop1
%o A249382 (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 A249382 Cf. A249383, A249384.
%K A249382 nonn
%O A249382 1,1
%A A249382 _Pierre CAMI_, Oct 27 2014