[go: up one dir, main page]

login
A244333
Number of ternary digits in the high-water marks of the terms of the continued fraction of the base 3 Champernowne constant (A077772).
2
0, 1, 1, 4, 5, 33, 139, 515, 1809, 6181, 20759, 68871, 226333, 738089, 2391459, 7705867, 24711977, 78918957, 251105839
OFFSET
1,4
FORMULA
It appears that: Define NCD(N)=3-N+(sum{m=1..(N-3)} 2*m*3^(m-1)); then for n>=5, a(n) = NCD(n)-2*NCD(n-1)-3*(n-2)+4.
PROG
(Ruby) puts (5..19).collect {|n| (1..(n-3)).inject(0) {|sum, m| sum+2*m*3**(m-1)}+3-n-2*((1..(n-4)).inject(0) {|sum1, m1| sum1+2*m1*3**(m1-1)}+3-(n-1))-3*(n-2)+4}
CROSSREFS
Cf. A077772 (Continued fraction expansion of the ternary Champernowne constant.)
Cf. A244757 (Incrementally largest terms in the continued fraction for the base 3 Champernowne constant.)
Cf. A244332 (Position of the incrementally largest term in the continued fraction for the base 3 Champernowne constant.)
Sequence in context: A013468 A376536 A378079 * A041907 A228662 A151450
KEYWORD
base,nonn,more
AUTHOR
John K. Sikora, Jun 27 2014
STATUS
approved