%I
%S 1,2,4,8,16,22,44,88,176,183,186,202,222,444,888,1776,1793,1802,1812,
%T 1823,1835,1840,1854,1869,1887,1974,1993,2006,2032,2055,2080,2108,
%U 2129,2158,2216,2432,2456,2501,2551,2602,2662,2724,2751,2822,2904,2994,3088,3118
%N a(n+1) = a(n) + smallest nonzero (and unused) integer embedded in a(n) as a (not necessarily contiguous) subchain.
%C The subchain numbers used are: 0, 1, 2, 4, 8, 6, 22, 44, 88, 7, 3, 16, 20, 222, 444, 888, 17, 9, 10, 11, 12, 5, 14, 15, 18, 87, 19, 13, 26, 23, 25, 28, 21, 29, ...
%H Hiroaki Yamanouchi, <a href="/A257350/b257350.txt">Table of n, a(n) for n = 1..100000</a>
%e After 186, the next term can be any of 186 + {1,8,6,18,16,86,186}, and 16 is the smallest of these that has not yet been used, so the next term is 186+16 = 202.
%t f[n_] := Block[{used = {0}, s = Table[1, {n}], k}, For[k = 2, k <= n, k++, s[[k]] = s[[k  1]] + SelectFirst[ FromDigits /@ Rest@ DeleteDuplicates@ Sort@ Subsets@ IntegerDigits@ s[[k  1]], ! MemberQ[used, #] &]; AppendTo[used, s[[k]]  s[[k  1]]] ]; s ]; f@36. (* If you want to see the "used" data as well, replace the "s" near the end of the function with "{s, used}" *)
%Y A variant of A257165.
%K nonn,base
%O 1,2
%A _JeanMarc Falcoz_, Apr 17 2015 and _Michael De Vlieger_, Apr 19 2015
%E a(35)a(48) from _Hiroaki Yamanouchi_, May 03 2015
