cp's OEIS Frontend

A191751 Least k such that (2^n-1)*2^n - k is a prime number.

%I A191751 #20 May 15 2020 04:38:58
%S A191751 0,1,3,1,1,5,3,11,1,1,25,29,3,13,3,7,39,1,13,23,3,5,69,11,39,13,15,31,
%T A191751 99,83,117,31,9,11,25,67,45,1,39,47,45,71,69,77,1,131,67,101,55,1,9,
%U A191751 41,13,43,33,233,1,113,7,29,45,55,99,41,261,5,15,343,9
%N A191751 Least k such that (2^n-1)*2^n - k is a prime number.
%H A191751 Jinyuan Wang, <a href="/A191751/b191751.txt">Table of n, a(n) for n = 1..1500</a> (terms 1..500 from Nathaniel Johnston)
%e A191751 a(1)=0 because (2^1-1)*2^1 - 0 =    2 is prime,
%e A191751 a(2)=1 because (2^2-1)*2^2 - 1 =   11 is prime,
%e A191751 a(3)=3 because (2^3-1)*2^3 - 3 =   53 is prime,
%e A191751 a(4)=1 because (2^4-1)*2^4 - 1 =  239 is prime,
%e A191751 a(5)=1 because (2^5-1)*2^5 - 1 =  991 is prime,
%e A191751 a(6)-5 because (2^6-1)*2^6 - 5 = 4027 is prime.
%p A191751 a := proc(n) local k: for k from 0 do if(isprime((2^n-1)*2^n-k))then return k: fi: od: end: seq(a(n), n=1..69); # _Nathaniel Johnston_, Jun 14 2011
%t A191751 lk[n_]:=Module[{c=2^n,k=0},While[!PrimeQ[c(c-1)-k],k++];k]; Array[lk,70] (* _Harvey P. Dale_, Jul 02 2018 *)
%o A191751 (PARI) a(n) = my(x=(2^n-1)*2^n); x - precprime(x); \\ _Michel Marcus_, Feb 21 2019
%Y A191751 Cf. A098845, A191001, A191620.
%Y A191751 Cf. A020522 ((2^n-1)*2^n).
%K A191751 nonn
%O A191751 1,3
%A A191751 _Juri-Stepan Gerasimov_, Jun 14 2011, Jun 15 2011