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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 n-th row = A007318(A003056(n-1),A002262(n-1));

1 <= i < j <= length of n-th 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: A239235 A031297 A239086 * A209862 A209861 A287929

Adjacent sequences:  A187766 A187767 A187768 * A187770 A187771 A187772

KEYWORD

nonn,base,tabf

AUTHOR

Reinhard Zumkeller, Jan 05 2013

STATUS

approved

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Last modified October 16 10:09 EDT 2018. Contains 316262 sequences. (Running on oeis4.)