A167755 - OEIS

%I #8 Feb 10 2022 03:34:15

%S 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,

%T 26,24,28,17,29,16,30,31,31,42,42,36,50,51,51,37,53,56,56,35,57,34,58,

%U 48,60,33,61,32,62,63,63

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

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

%e After the initial zero, A037016 begins:

%e   1

%e   2 3

%e   5 6 7

%e   10 12 13 14 15

%e   21 25 26 28 29 30 31

%e   42 50 51 53 56 57 58 60 61 62 63

%e   85 ...

%e and after resorting, A175020 begins:

%e   1

%e   2 3

%e   5 4 7

%e   10 12 9 8 15

%e   21 ...

%e so the irregular table begins:

%e   1 1

%e   2 2 3 3

%e   5 5 4 6 7 7

%e   10 10 12 12 9 13 8 14 15 15

%e   etc.

%e 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.

%Y Cf. A000041 (1/2 row length of the irregular Table). A000975 (first & second column).

%K nonn,tabf,uned

%O 1,3

%A _Alford Arnold_, Nov 10 2009