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A250745 Start with a(1) = 1; then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(1), a(2), ..., a(n)).

%I A250745 #11 Dec 10 2014 03:57:52
%S A250745 1,2,3,5,10,4,8,6,11,20,13,7,9,12,15,18,14,25,30,24,16,32,40,29,50,
%T A250745 100,26,52,39,21,28,35,42,17,34,51,23,46,27,36,45,43,19,38,68,48,60,
%U A250745 75,90,54,56,58,22,44,33,55,97,125,200,64,80,69,66,88,70,41,82
%N A250745 Start with a(1) = 1; then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(1), a(2), ..., a(n)).
%C A250745 Like A171785 but without the constraint a(n) > a(n-1).
%C A250745 Among the first 1000 terms, a(n) = n for n = 1, 2, 3, 15, 170, 577, 759, and the numbers not yet found are 149, 298, 347, 401, 447, 454, 457, 467, 487, 509, etc.
%C A250745 Is this sequence a rearrangement of the natural numbers?
%H A250745 Paolo P. Lava, <a href="/A250745/b250745.txt">Table of n, a(n) for n = 1..1000</a>
%e A250745 a(1) = 1;
%e A250745 a(2) = 2 -> 12 /2 = 6;
%e A250745 a(3) = 3 -> 123 / 3 = 41;
%e A250745 Then we cannot use 4 as the next term because 1234 / 4 = 617 / 2.
%e A250745 a(4) = 5 -> 1235 / 5 = 247;
%e A250745 Again, 4, 6, 7, 8 and 9 cannot be used as the next term.
%e A250745 a(5) = 10 -> 123510 / 10 = 12351;
%e A250745 a(6) = 4 -> 1235104 / 4 = 308776;
%e A250745 a(7) = 8 -> 12351048 / 8 = 1543881; etc.
%p A250745 with(numtheory); P:=proc(q) local a,b,k,n; a:=0; b:={};
%p A250745 for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
%p A250745 then if type((a*10^(1+ilog10(n))+n)/n,integer)
%p A250745 then a:=a*10^(1+ilog10(n))+n; b:= b union {n}; print(n); break;
%p A250745 fi; fi; od; od; end: P(10^5);
%Y A250745 Cf. A171785, A240588, A241811, A249398, A249399, A250746, A250747.
%K A250745 nonn,base
%O A250745 1,2
%A A250745 _Paolo P. Lava_, Nov 27 2014