|
|
A086593
|
|
Bisection of A086592, denominators of the left-hand half of Kepler's tree of fractions.
|
|
6
|
|
|
2, 3, 4, 5, 5, 7, 7, 8, 6, 9, 10, 11, 9, 12, 11, 13, 7, 11, 13, 14, 13, 17, 15, 18, 11, 16, 17, 19, 14, 19, 18, 21, 8, 13, 16, 17, 17, 22, 19, 23, 16, 23, 24, 27, 19, 26, 25, 29, 13, 20, 23, 25, 22, 29, 26, 31, 17, 25, 27, 30, 23, 31, 29, 34, 9, 15, 19, 20, 21, 27, 23, 28, 21, 30
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(2^(m+1)+k+1) - a(2^m+k+1) = A071585(k), m >= 0, 0 <= k < 2^m.
a(2^(m+2)-k) = a(2^(m+1)-k) + a(2^m-k), m > 0, 0 <= k < 2^m-1.
(End)
|
|
MATHEMATICA
|
(* b = A020650 *) b[1] = 1; b[2] = 2; b[3] = 1; b[n_] := b[n] = Switch[ Mod[n, 4], 0, b[n/2 + 1] + b[n/2], 1, b[(n - 1)/2 + 1], 2, b[(n - 2)/2 + 1] + b[(n - 2)/2], 3, b[(n - 3)/2]]; a[1] = 2; a[n_] := b[4 n - 4]; Array[a, 100] (* Jean-François Alcover, Jan 22 2016, after Yosu Yurramendi's formula for A020650 *)
|
|
PROG
|
(R)
maxlevel <- 15
d <- c(1, 2)
for(m in 0:maxlevel)
for(k in 1:2^m) {
d[2^(m+1) +k] <- d[k] + d[2^m+k]
d[2^(m+1)+2^m+k] <- d[2^(m+1)+k]
}
a <- vector()
for(m in 0:maxlevel) for(k in 0:(2^m-1)) a[2^m+k] <- d[2^(m+1)+k]
a[1:63]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|