

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.


3



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 nth row = A007318(A003056(n1),A002262(n1));
1 <= i < j <= length of nth row: A023416(T(n,i)) = A023416(T(n,j)), A000120(T(n,i)) = A000120(T(n,j)) and A070939(T(n,i)) = A070939(T(n,j));
the table provides a permutation of the natural numbers when seen as flattened sequence.


LINKS

Reinhard Zumkeller, Rows n = 0..78 of triangle, flattened  all terms < 2^12
Reinhard Zumkeller, Illustration of initial terms
Index entries for sequences related to binary expansion of n
Index entries for triangles and arrays related to Pascal's triangle
Index entries for sequences that are permutations of the natural numbers


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;
cf. A099627 (left edge), A023758 (right edge).
Sequence in context: A031297 A239086 A306866 * A209862 A209861 A287929
Adjacent sequences: A187766 A187767 A187768 * A187770 A187771 A187772


KEYWORD

nonn,base,tabf


AUTHOR

Reinhard Zumkeller, Jan 05 2013


STATUS

approved



