cp's OEIS Frontend

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

%I A167755 #8 Feb 10 2022 03:34:15
%S A167755 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 A167755 26,24,28,17,29,16,30,31,31,42,42,36,50,51,51,37,53,56,56,35,57,34,58,
%U A167755 48,60,33,61,32,62,63,63
%N A167755 Match the multisets in A175020 with those in A037016 then merge the two sequences.
%C A167755 A175020 records the multiset with minimum value; whereas A037016 is based on reading binary expansion from right to left, run lengths increase.
%e A167755 After the initial zero, A037016 begins:
%e A167755   1
%e A167755   2 3
%e A167755   5 6 7
%e A167755   10 12 13 14 15
%e A167755   21 25 26 28 29 30 31
%e A167755   42 50 51 53 56 57 58 60 61 62 63
%e A167755   85 ...
%e A167755 and after resorting, A175020 begins:
%e A167755   1
%e A167755   2 3
%e A167755   5 4 7
%e A167755   10 12 9 8 15
%e A167755   21 ...
%e A167755 so the irregular table begins:
%e A167755   1 1
%e A167755   2 2 3 3
%e A167755   5 5 4 6 7 7
%e A167755   10 10 12 12 9 13 8 14 15 15
%e A167755   etc.
%e A167755 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 A167755 Cf. A000041 (1/2 row length of the irregular Table). A000975 (first & second column).
%K A167755 nonn,tabf,uned
%O A167755 1,3
%A A167755 _Alford Arnold_, Nov 10 2009