login
Least k such that k*2^n - 1 is a semiprime.
1

%I #8 Jul 01 2020 23:08:56

%S 5,4,2,1,3,5,4,2,1,2,1,3,6,3,3,3,3,6,3,3,3,2,1,3,6,3,6,3,6,3,3,11,16,

%T 8,4,2,1,8,4,2,1,15,13,15,16,8,4,2,1,6,3,17,15,12,6,3,4,2,1,3,6,3,3,5,

%U 3,2,1,5,6,3,48,24,12,6,3,12,6,3,10,5,4,2,1,3,3,31,21,17,15,11,13,24,12,6,3

%N Least k such that k*2^n - 1 is a semiprime.

%C The first few values of n such that 509203*2^n - 1 is a semiprime, where k = 509203 (the conjectured smallest Riesel number), are: 3,4,16,34,61,82,124,142,163,171,... Conjecture: there are infinitely many semiprimes of this form.

%H Sean A. Irvine, <a href="/A085917/b085917.txt">Table of n, a(n) for n = 1..500</a>

%e a(33)=16 because k*2^33 - 1 is not a semiprime for k=1,2,...15, but 16*2^33 - 1 = 223 * 616318177 is.

%Y Cf. A001358, A085427, A076337, A085245.

%K nonn

%O 1,1

%A _Jason Earls_, Aug 16 2003