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A167755
Match the multisets in A175020 with those in A037016 then merge the two sequences.
0
1, 1, 2, 2, 3, 3, 5, 5, 4, 6, 7, 7, 10, 10, 12, 12, 9, 13, 8, 14, 15, 15, 21, 21, 19, 25, 18, 26, 24, 28, 17, 29, 16, 30, 31, 31, 42, 42, 36, 50, 51, 51, 37, 53, 56, 56, 35, 57, 34, 58, 48, 60, 33, 61, 32, 62, 63, 63
OFFSET
1,3
COMMENTS
A175020 records the multiset with minimum value; whereas A037016 is based on reading binary expansion from right to left, run lengths increase.
EXAMPLE
After the initial zero, A037016 begins:
1
2 3
5 6 7
10 12 13 14 15
21 25 26 28 29 30 31
42 50 51 53 56 57 58 60 61 62 63
85 ...
and after resorting, A175020 begins:
1
2 3
5 4 7
10 12 9 8 15
21 ...
so the irregular table begins:
1 1
2 2 3 3
5 5 4 6 7 7
10 10 12 12 9 13 8 14 15 15
etc.
In binary, the number 9 maps to multiset (1,2,1) and the number 13 maps to (2,1,1), so 9 and 13 appear together in the sequence.
CROSSREFS
Cf. A000041 (1/2 row length of the irregular Table). A000975 (first & second column).
Sequence in context: A139807 A308465 A276119 * A259788 A033302 A072729
KEYWORD
nonn,tabf,uned
AUTHOR
Alford Arnold, Nov 10 2009
STATUS
approved