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