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

Author

Alford Arnold, Nov 10 2009

Keywords

• nonn
• tabf
• uned

Comments

A175020 records the multiset with minimum value; whereas A037016 is based on reading binary expansion from right to left, run lengths increase.

Examples

			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).