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A249806 Smallest odd number k>1 such that k*2^prime(n)-1 is also prime.

%I A249806 #10 Apr 25 2016 11:50:04
%S A249806 3,3,7,3,3,9,7,51,13,7,15,21,15,3,31,147,45,69,43,73,15,69,91,19,51,
%T A249806 81,3,25,9,85,103,55,169,225,109,145,15,103,615,69,259,69,63,45,285,
%U A249806 471,9,255,169,489,69,273,427,43,391,169,201,21
%N A249806 Smallest odd number k>1 such that k*2^prime(n)-1 is also prime.
%C A249806 If prime(n) is a Mersenne prime exponent then 2^prime(n)-1 is a prime < k*2^prime(n)-1.
%H A249806 Pierre CAMI, <a href="/A249806/b249806.txt">Table of n, a(n) for n = 1..1000</a>
%p A249806 3*2^2-1=11 prime so a(1)=3.
%p A249806 3*2^3-1=23 prime so a(2)=3.
%p A249806 3*2^5-1=95 composite, 5*2^5-1=159 composite, 7*2^5-1=223 prime so a(3)=7.
%t A249806 a249806[n_Integer] := Catch[Module[{k}, For[k = 3, k < 10^5, k += 2, If[PrimeQ[k*2^Prime[n] - 1], Throw[k], 0]]]]; a249806 /@ Range[120] (* _Michael De Vlieger_, Nov 11 2014 *)
%o A249806 (PFGW & SCRIPT)
%o A249806 SCRIPT
%o A249806 DIM j,0
%o A249806 DIM k
%o A249806 DIM n
%o A249806 DIMS t
%o A249806 OPENFILEOUT myf,a(n).txt
%o A249806 LABEL loop1
%o A249806 SET j,j+1
%o A249806 IF j>1000 THEN END
%o A249806 SET k,p(j)
%o A249806 SET n,1
%o A249806 LABEL loop2
%o A249806 SET n,n+2
%o A249806 SETS t,%d,%d,%d\,;j;k;n
%o A249806 PRP n*2^k-1,t
%o A249806 IF ISPRP THEN GOTO a
%o A249806 GOTO loop2
%o A249806 LABEL a
%o A249806 WRITE myf,t
%o A249806 GOTO loop1
%o A249806 (PARI) s=[]; forprime(p=2, 500, k=3; q=2^p; while(!ispseudoprime(k*q-1), k+=2); s=concat(s, k)); s \\ _Colin Barker_, Nov 06 2014
%Y A249806 Cf. A135434.
%K A249806 nonn
%O A249806 1,1
%A A249806 _Pierre CAMI_, Nov 06 2014