|
|
A187769
|
|
Triangle read by rows: equivalence classes of natural numbers, where numbers are equivalent when having equal numbers of zeros and ones in binary representation, respectively.
|
|
7
|
|
|
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 13, 14, 15, 16, 17, 18, 20, 24, 19, 21, 22, 25, 26, 28, 23, 27, 29, 30, 31, 32, 33, 34, 36, 40, 48, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 47, 55, 59, 61, 62, 63, 64, 65, 66
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Row lengths are given by Pascal's triangle (cf. A007318), seen as flattened sequence, or for n > 0: length of n-th row = A007318(A003056(n-1),A002262(n-1));
the table provides a permutation of the natural numbers when seen as flattened sequence.
|
|
LINKS
|
|
|
EXAMPLE
|
See link.
|
|
PROG
|
(Haskell)
import List (elemIndices)
a187769 n k = a187769_tabf !! n !! k
a187769_row n = a187769_tabf !! n
a187769_tabf = [0] : [elemIndices (b, len - b) $
takeWhile ((<= len) . uncurry (+)) $ zip a000120_list a023416_list |
len <- [1 ..], b <- [1 .. len]]
a187769_list = concat a187769_tabf
|
|
CROSSREFS
|
Rows of A187786, duplicates removed;
|
|
KEYWORD
|
nonn,base,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|