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A249398 Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n-1),a(n)).

%I A249398 #8 Dec 10 2014 03:59:12
%S A249398 1,2,4,5,10,20,25,50,100,125,200,250,400,500,625,1000,1250,2000,2500,
%T A249398 3125,5000,6250,10000,12500,15625,20000,25000,31250,40000,50000,62500,
%U A249398 78125,100000,125000,156250,200000,250000,312500,390625,500000,625000,781250,1000000
%N A249398 Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n-1),a(n)).
%H A249398 Paolo P. Lava, <a href="/A249398/b249398.txt">Table of n, a(n) for n = 1..100</a>
%e A249398 a(1) = 1;
%e A249398 a(2) = 2 -> 12 /2 = 6;
%e A249398 Now we cannot use 3 as the next term because it does not divide 23.
%e A249398 a(3) = 4 -> 24 / 4 = 6;
%e A249398 a(4) = 5 -> 45 / 5 = 9;
%e A249398 Again, 6, 7, 8 and 9 cannot be used as the next term.
%e A249398 a(5) = 10 -> 510 / 10 = 51;
%e A249398 a(6) = 20 -> 1020 / 20 = 51;
%e A249398 a(7) = 25 -> 2025 / 25 = 81; etc.
%p A249398 with(numtheory); P:=proc(q) local a,k,n; print(1); a:=1;
%p A249398 for n from 2 to q do if type((a*10^(1+ilog10(n))+n)/n,integer)
%p A249398 then a:=n; print(n); fi; od; end: P(10^12);
%Y A249398 Cf. A171785, A249399, A250745, A250746, A250747.
%K A249398 nonn,base
%O A249398 1,2
%A A249398 _Paolo P. Lava_, Dec 01 2014