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A250747 Start with a(0) = 0; then a(n) = smallest number not already in the sequence such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

%I A250747 #16 Dec 10 2014 03:58:29
%S A250747 0,1,2,3,5,10,6,9,13,26,15,18,30,431,73,67,134,7,14,21,35,29,58,127,
%T A250747 27,39,43,70,11,22,19,38,95,190,2748070932534311,2768821759897,
%U A250747 5537643519794,787,191,382,955,17,31,45,54,90,101,202,303,57,114,47,55,33,66
%N A250747 Start with a(0) = 0; then a(n) = smallest number not already in the sequence such that a(n) divides concat(a(n), a(n-1), ..., a(0)).
%C A250747 Like A250746, but without the constraint a(n) > a(n-1).
%H A250747 Jon E. Schoenfield, <a href="/A250747/b250747.txt">Table of n, a(n) for n = 0..165</a>
%e A250747 a(0) = 0;
%e A250747 a(1) = 1 -> 10 / 1 = 10;
%e A250747 a(2) = 2 -> 210 / 2 = 105;
%e A250747 a(3) = 3 -> 3210 / 3 = 1070;
%e A250747 Now we cannot use 4 as the next term because 43210 / 4 = 21605 / 2.
%e A250747 a(4) = 5 -> 32105 / 5 = 6421;
%e A250747 Again, we cannot use 4, 6, 7, 8 or 9.
%e A250747 a(5) = 10 -> 1053210 / 10 = 105321.
%e A250747 We still cannot use 4, but 6 is ok.
%e A250747 a(6) = 6 -> 61053210 / 6 = 10175535. Etc.
%p A250747 with(numtheory); P:=proc(q) local a,b,k,n; print(0); print(1); a:=10; b:={0,1};
%p A250747 for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
%p A250747 then if type((n*10^(1+ilog10(a))+a)/n,integer)
%p A250747 then a:=n*10^(1+ilog10(a))+a; b:= b union {n}; print(n); break; fi; fi;
%p A250747 od; od; end: P(10^5);
%Y A250747 Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250746.
%K A250747 nonn,base
%O A250747 0,3
%A A250747 _Paolo P. Lava_, Nov 28 2014
%E A250747 More terms from _Jon E. Schoenfield_, Nov 29 2014