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%I #20 Jan 22 2017 06:38:05
%S 2,3,4,5,7,18,35,52,168,335,502,1668,3335,5002,14287,16668,33335,
%T 50002,166668,333335,500002,1666668,3333335,5000002,16666668,33333335,
%U 50000002,166666668,333333335,500000002,1666666668,3333333335
%N Numbers k such that k-1 | concat(k, k+1).
%C Numbers of the form 10^(j+1) + 60*(10^j-1)/9 + 8, 30*(10^j-1)/9 + 5 and 5*10^j + 2, for j>=0, belong to the sequence.
%C The ratios are: 23, 17, 15, 14, 13, 107, 104, 103, 1007, 1004, 1003, 10007, 10004, 10003, 100008, 100007, 100004, 100003, 1000007, 1000004, 1000003, 10000007, 10000004, 10000003, 100000007, 100000004, 100000003, 1000000007, 1000000004, 1000000003, ...
%F a(n) = A069860(n) + 1. - _Alois P. Heinz_, Jan 19 2017
%e concat(2,3) / 1 = 23 / 1 = 23; concat(3,4) / 2 = 34 / 2 = 17; etc.
%p with(numtheory): P:=proc(q) local c,n;
%p for n from 2 to q do c:=n*10^(ilog10(n+1)+1)+n+1;
%p if type(c/(n-1),integer) then print(n); fi; od; end: P(10^9)
%t Select[Range[2, 10^7], Divisible[FromDigits@ Flatten@ Map[IntegerDigits, {#, # + 1}], # - 1] &] (* _Michael De Vlieger_, Jan 19 2017 *)
%Y Cf. A069860, A281232, A069871.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Jan 18 2017
%E Two more terms (using A069860) from _Alois P. Heinz_, Jan 19 2017
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