A167755 Match the multisets in A175020 with those in A037016 then merge the two sequences.

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.

Links

Table of n, a(n) for n=1..58.

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

Adjacent sequences: A167752 A167753 A167754 * A167756 A167757 A167758

Keyword

nonn,tabf,uned

Author

Alford Arnold, Nov 10 2009

Status

approved