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%I #8 Feb 02 2014 01:21:10
%S 1,2,2,1,2,2,2,3,2,4,2,5,2,6,2,6,1,2,6,2,2,6,3,2,6,4,2,6,5,2,6,6,2,6,
%T 7,2,6,8,2,6,9,2,6,10,2,6,10,1,2,6,10,2,2,6,10,3,2,6,10,4,2,6,10,5,2,
%U 6,10,6,2,6,10,7
%N Distribution of the natural numbers using the sequences family mentioned in the comments.
%C Based on A016825=2,6,10,..., the family is
%C N16(1)=1, followed by 2's =A040000,
%C N16(2)=1,2,3,4,5, followed by 6's =A101272,
%C N16(3)=1,2,3,4,5,6,7,8,9, followed by 10's, not in the OEIS,
%C N16(4)=1,2,3,4,5,6,7,8,9,10,11,12,13, followed by 14's, idem.
%C The N16(n) gives the successive columns beginning at row 1, 3, 9, 19, ... =A058331.
%C Sum of every row: n =A000027.
%C Note that with only N16(1),
%C 1,
%C 2,
%C 2, 1,
%C 2, 2,
%C 2, 2, 1,
%C 2, 2, 2,
%C 2, 2, 2, 1,
%C 2, 2, 2, 2,
%C 2, 2, 2, 2, 1, etc
%C is A169695(n+1).
%C A169695(n) corresponds to A028310.
%e 1,
%e 2,
%e 2, 1,
%e 2, 2,
%e 2, 3,
%e 2, 4,
%e 2, 5,
%e 2, 6,
%e 2, 6, 1,
%e 2, 6, 2,
%e 2, 6, 3,
%e 2, 6, 4, etc.
%Y Cf. A173642.
%K nonn,uned
%O 1,2
%A _Paul Curtz_, Dec 25 2013
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