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A250746 Start with a(0) = 0; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

%I A250746 #30 Jun 13 2018 03:44:05
%S A250746 0,1,2,3,5,10,15,18,19,35,42,51,55,70,85,93,95,106,155,217,310,745,
%T A250746 1210,1342,3355,5185,6222,6330,9495,10413,11115,12070,13774,34435,
%U A250746 41322,61983,68870,1601065116264571,2217993924228622,2324778503347862,2325380783693255
%N A250746 Start with a(0) = 0; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n), a(n-1), ..., a(0)).
%C A250746 This sequence is infinite. - _Robert G. Wilson v_, Dec 09 2014
%H A250746 Robert G. Wilson v, <a href="/A250746/b250746.txt">Table of n, a(n) for n = 0..46</a>
%e A250746 a(0) = 0;
%e A250746 a(1) = 1 -> 10 / 1 = 10;
%e A250746 a(2) = 2 -> 210 / 2 = 105;
%e A250746 a(3) = 3 -> 3210 / 3 = 1070;
%e A250746 Now we cannot use 4 as the next term because 43210 / 4 = 21605 / 2.
%e A250746 a(4) = 5 -> 32105 / 5 = 6421; etc.
%p A250746 with(numtheory); P:=proc(q) local a,k,n; print(0); print(1); a:=10;
%p A250746 for n from 2 to q do if type((n*10^(1+ilog10(a))+a)/n,integer)
%p A250746 then a:=n*10^(1+ilog10(a))+a; print(n);
%p A250746 fi; od; end: P(10^9);
%t A250746 f[lst_List] := Block[{k = lst[[-1]] + 1, id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, While[ Mod[ id, k] > 0, k++]; Append[lst, k]]; Nest[f, {0}, 36] (* or *)
%t A250746 f[lst_List] := Block[{mn = lst[[-1]], id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, d = Divisors@ id; Append[lst, Min@ Select[d, # > mn &]]]; Nest[f, {0, 1}, 36] (* _Robert G. Wilson v_, Dec 08 2014 *)
%Y A250746 Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250747.
%K A250746 nonn,base
%O A250746 0,3
%A A250746 _Paolo P. Lava_, Nov 27 2014
%E A250746 a(37)-a(40) from _Robert G. Wilson v_, Dec 08 2014