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

%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