A250746 - OEIS

%I #30 Jun 13 2018 03:44:05

%S 0,1,2,3,5,10,15,18,19,35,42,51,55,70,85,93,95,106,155,217,310,745,

%T 1210,1342,3355,5185,6222,6330,9495,10413,11115,12070,13774,34435,

%U 41322,61983,68870,1601065116264571,2217993924228622,2324778503347862,2325380783693255

%N 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 This sequence is infinite. - _Robert G. Wilson v_, Dec 09 2014

%H Robert G. Wilson v, <a href="/A250746/b250746.txt">Table of n, a(n) for n = 0..46</a>

%e a(0) = 0;

%e a(1) = 1 -> 10 / 1 = 10;

%e a(2) = 2 -> 210 / 2 = 105;

%e a(3) = 3 -> 3210 / 3 = 1070;

%e Now we cannot use 4 as the next term because 43210 / 4 = 21605 / 2.

%e a(4) = 5 -> 32105 / 5 = 6421; etc.

%p with(numtheory); P:=proc(q) local a,k,n; print(0); print(1); a:=10;

%p for n from 2 to q do if type((n*10^(1+ilog10(a))+a)/n,integer)

%p then a:=n*10^(1+ilog10(a))+a; print(n);

%p fi; od; end: P(10^9);

%t 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 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 Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250747.

%K nonn,base

%O 0,3

%A _Paolo P. Lava_, Nov 27 2014

%E a(37)-a(40) from _Robert G. Wilson v_, Dec 08 2014