|
|
A143534
|
|
Number of decimal digits in the high-water marks of the terms of the continued fraction of the (base-10) Champernowne constant.
|
|
2
|
|
|
0, 1, 1, 6, 166, 2504, 33102, 411100, 4911098, 57111096, 651111094, 7311111092
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
LINKS
|
|
|
FORMULA
|
It appears that: For N>=3, define NCD(N)=3-N+(sum{m=1..(N-3), m>0} 9*m*10^(m-1)); then for n>=4, a(n) = NCD(n) - 2*NCD(n-1) - 3*(n-2) + 4. - John K. Sikora, Aug 25 2012
|
|
PROG
|
(Ruby) puts (4..13).collect {|n| (1..(n-3)).inject(0) {|sum, m| sum+9*m*10**(m-1)}+3-n-2*((1..(n-4)).inject(0) {|sum1, m1| sum1+9*m1*10**(m1-1)}+3-(n-1))-3*(n-2)+4} # John K. Sikora, Aug 25 2012
|
|
CROSSREFS
|
Cf. A038705 (position of the incrementally largest term in continued fraction for Champernowne constant).
|
|
KEYWORD
|
nonn,more,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|