Search: a187786 -id:a187786
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A187769
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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.
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+10
7
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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)
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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See link.
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PROG
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(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
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CROSSREFS
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Rows of A187786, duplicates removed;
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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A361478
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Irregular table T(n, k), n >= 0, k = 1..A361477(n), read by rows; the n-th row lists the integers whose binary expansions have the same multiset of run-lengths as that of n.
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+10
4
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0, 1, 2, 3, 4, 6, 5, 4, 6, 7, 8, 14, 9, 11, 13, 10, 9, 11, 13, 12, 9, 11, 13, 8, 14, 15, 16, 30, 17, 23, 29, 18, 20, 22, 26, 19, 25, 27, 18, 20, 22, 26, 21, 18, 20, 22, 26, 17, 23, 29, 24, 28, 19, 25, 27, 18, 20, 22, 26, 19, 25, 27, 24, 28, 17, 23, 29, 16, 30
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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This sequence has similarities with A187786; here we consider multisets of run-lengths, there multisets of digits in binary expansions.
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LINKS
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FORMULA
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EXAMPLE
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Table T(n, k) begins (in decimal and in binary):
n n-th row bin(n) n-th row in binary
-- ---------- ------ ------------------
0 0 0 0
1 1 1 1
2 2 10 10
3 3 11 11
4 4, 6 100 100, 110
5 5 101 101
6 4, 6 110 100, 110
7 7 111 111
8 8, 14 1000 1000, 1110
9 9, 11, 13 1001 1001, 1011, 1101
10 10 1010 1010
11 9, 11, 13 1011 1001, 1011, 1101
12 12 1100 1100
13 9, 11, 13 1101 1001, 1011, 1101
14 8, 14 1110 1000, 1110
15 15 1111 1111
16 16, 30 10000 10000, 11110
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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