login
Least number requiring n terms to express it as a sum of signed terms of the form 2^k-1.
0

%I #8 Mar 31 2012 10:27:21

%S 1,2,5,20,83,594,2641,10856,43623,305766,1354341,5548644,22325859,

%T 89434722,357870241,1431612752,5726580047

%N Least number requiring n terms to express it as a sum of signed terms of the form 2^k-1.

%C a(n) = min{ i : A192099(i) = n }

%C Conjecture: a(n) = (4^n)/3 + O(1).

%H <a href="http://www.crm.umontreal.ca/CanaDAM2009/pdf/ruskey.pdf">Isoperimetric sequences for infinite complete binary trees and their relation to meta-Fibonacci sequences and signed almost binary partitions</a>, talk at CANADAM, 2009.

%e The smallest value of i for which A192099(i) = 5 is 83 = 31+15+7-3+1, and so a(5) = 83.

%Y Cf. A192099.

%K nonn,more

%O 1,2

%A _Frank Ruskey_, Jul 29 2011