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A229927 Smallest k >= n such that (4^n-1)*2^k - 1 is prime.

%I A229927 #19 Jul 30 2020 20:16:02
%S A229927 1,2,3,4,8,6,7,13,11,16,103,12,16,52,26,16,26,34,38,28,23,22,26,24,50,
%T A229927 41,30,28,32,46,31,34,202,34,35,40,47,113,46,50,44,54,58,46,51,48,130,
%U A229927 59,64,101,60,62,94,74,88,98,71,234,67,93,83,101,308,64,92
%N A229927 Smallest k >= n such that (4^n-1)*2^k - 1 is prime.
%C A229927 Conjecture: there is no "Riesel" number of the form 4^n-1; that is, a(n) exists for all n.
%H A229927 Pierre CAMI, <a href="/A229927/b229927.txt">Table of n, a(n) for n = 1..2500</a>
%e A229927 (4^1-1)*2^1-1=5 prime so a(1)=1.
%e A229927 (4^2-1)*2^2-1=59 prime so a(2)=2.
%t A229927 sk[n_]:=Module[{k=n,c=4^n-1},While[!PrimeQ[c*2^k-1],k++];k]; Array[sk,70] (* _Harvey P. Dale_, Jul 30 2020 *)
%o A229927 PFGW & SCRIPTIFY
%o A229927 SCRIPT
%o A229927 DIM k
%o A229927 DIM n,0
%o A229927 DIMS tt
%o A229927 OPENFILEOUT myf,a(n).txt
%o A229927 LABEL a
%o A229927 SET n,n+1
%o A229927 IF n>2500 THEN END
%o A229927 SET k,n-1
%o A229927 LABEL b
%o A229927 SET k,k+1
%o A229927 SETS tt,%d,%d\,;n;k
%o A229927 PRP (4^n-1)*2^k-1,tt
%o A229927 IF ISPRP THEN GOTO c
%o A229927 GOTO b
%o A229927 LABEL c
%o A229927 WRITE myf,tt
%o A229927 GOTO a
%Y A229927 Cf. A098845.
%K A229927 nonn
%O A229927 1,2
%A A229927 _Pierre CAMI_, Oct 03 2013