cp's OEIS Frontend

A210733 Least k > n-1 such that 4^n + 2^k - 1 is a prime number.

%I A210733 #19 Feb 24 2018 11:55:34
%S A210733 1,2,3,4,6,6,12,9,10,10,27,13,15,22,16,16,18,19,39,22,22,43,24,24,48,
%T A210733 26,28,43,32,38,75,33,36,58,35,57,55,47,48,52,54,72,52,51,72,54,72,53,
%U A210733 64,62,52,52,63,60,55,60,316,70,63,68,64,96,66,115,66,92
%N A210733 Least k > n-1 such that 4^n + 2^k - 1 is a prime number.
%C A210733 As n increases k is on average 1.43*n.
%H A210733 Pierre CAMI, <a href="/A210733/b210733.txt">Table of n, a(n) for n = 1..3867</a>
%e A210733 4^1+2^1-1=5 prime so a(1)=1.
%e A210733 4^2+2^2-1=19 prime so a(2)=2.
%e A210733 4^3+2^3-1=71 prime so a(3)=3.
%t A210733 Table[k = n; While[! PrimeQ[4^n + 2^k - 1], k++];  k, {n, 100}] (* _T. D. Noe_, May 16 2012 *)
%o A210733 (PFGW64 and SCRIPTIFY)
%o A210733 Command : PFGW64 -f in.txt
%o A210733 in.txt file :
%o A210733 SCRIPT
%o A210733 DIM nn,0
%o A210733 DIM kk
%o A210733 DIMS tt
%o A210733 OPENFILEOUT myfile,a(n).txt
%o A210733 LABEL loopn
%o A210733 SET nn,nn+1
%o A210733 SET kk,nn-1
%o A210733 LABEL loopk
%o A210733 SET kk,kk+1
%o A210733 SETS tt,%d,%d\,;nn;kk
%o A210733 PRP 4^nn+2^kk-1,tt
%o A210733 IF ISPRP THEN GOTO a
%o A210733 IF ISPRIME THEN GOTO a
%o A210733 GOTO loopk
%o A210733 LABEL a
%o A210733 WRITE myfile,tt
%o A210733 GOTO loopn
%K A210733 nonn
%O A210733 1,2
%A A210733 _Pierre CAMI_, May 10 2012
%E A210733 Missing a(2103) inserted into b-file by _Andrew Howroyd_, Feb 24 2018