%I #26 Apr 25 2016 11:50:02
%S 2,2,2,3,13,2,7,2,2,3,79,5,83,1427,2,83,47,7,31,139,23,53,7,373,193,
%T 71,5,3,463,2,3,13,281,3,281,59,17,13,1399,7,61,163,151,2,103,479,89,
%U 5,127,421,457,857,2,43,101,349,359,2243,13,13,17,1451,2
%N Smallest prime number P such that 2*P^(2*n)-1 is a prime number.
%C a(n) = 2 when 2*n + 1 is a prime Mersenne exponent (A000043).
%H Pierre CAMI, <a href="/A240166/b240166.txt">Table of n, a(n) for n = 1..700</a>
%e 2*2^(2*1) - 1 = 7 prime so a(1) = 2.
%e 2*2^(2*2) - 1 = 31 prime so a(2) = 2.
%e 2*2^(2*3) - 1 = 127 prime so a(3) = 2.
%p A:= proc(n)
%p local p;
%p p:= 2;
%p while not isprime(2*p^(2*n)-1) do p:= nextprime(p) od:
%p p;
%p end proc:
%p seq(A(n),n=1..100); # _Robert Israel_, Sep 14 2014
%t a240166[n_Integer] := Module[{p = 1},
%t While[! PrimeQ[2*Prime[p]^(2*n) - 1], p++]; Prime[p]]; a240166 /@ Range[120] (* _Michael De Vlieger_, Aug 12 2014 *)
%o (PFGW & SCRIPT)
%o SCRIPT
%o DIM i
%o DIM n,0
%o DIM k
%o DIMS t
%o OPENFILEOUT myf,a(n).txt
%o LABEL loop1
%o SET n,n+1
%o SET i,0
%o LABEL loop2
%o SET i,i+1
%o SETS t,%d,%d\ ;n;p(i)
%o PRP 2*p(i)^(2*n)-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) = p=2; while(!ispseudoprime(2*p^(2*n)-1), p=nextprime(p+1)); p
%o vector(70, n, a(n)) \\ _Colin Barker_, Aug 02 2014
%Y Cf. A000043.
%K nonn
%O 1,1
%A _Pierre CAMI_, Aug 02 2014