OFFSET
1,3
COMMENTS
Conjecture: partial sums of A296965 (equivalent to observation about A183155 below). - Sean A. Irvine, Jul 16 2022
LINKS
John K. Sikora, Table of n, a(n) for n = 1..24
John K. Sikora, Analysis of the High Water Mark Convergents of Champernowne's Constant in Various Bases, arXiv:1408.0261 [math.NT]
FORMULA
It appears that for n >= 4, a(n) = 2^n - 2*n + 1 = A183155(n-1).
Also it appears that if we define NCD(N) = (Sum_{m=1..N} m*2^(m-1)) - N, then for n >= 4, a(n) = NCD(n) - 2*NCD(n-1) - 3*n + 4.
PROG
(Ruby) puts (4..24).collect{|n| 2**n-2*n+1}
(Ruby) puts (4..24).collect {|n| (1..n).inject(0) {|sum, m| sum+m*2**(m-1)}-n-2*((1..(n-1)).inject(0) {|sum1, m1| sum1+m1*2**(m1-1)}-(n-1))-3*n+4}
CROSSREFS
KEYWORD
base,nonn,more
AUTHOR
John K. Sikora, Jun 27 2014
STATUS
approved