A281233 Numbers k such that k-1 | concat(k, k+1).

2, 3, 4, 5, 7, 18, 35, 52, 168, 335, 502, 1668, 3335, 5002, 14287, 16668, 33335, 50002, 166668, 333335, 500002, 1666668, 3333335, 5000002, 16666668, 33333335, 50000002, 166666668, 333333335, 500000002, 1666666668, 3333333335

Offset: 1

Author

Paolo P. Lava, Jan 18 2017

Keywords

• nonn
• base
• more

Comments

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.

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, ...

Examples

			concat(2,3) / 1 = 23 / 1 = 23; concat(3,4) / 2 = 34 / 2 = 17; etc.
		

Crossrefs

Cf. A069860, A281232, A069871.

Programs

Maple

with(numtheory): P:=proc(q) local c,n;
for n from 2 to q do c:=n*10^(ilog10(n+1)+1)+n+1;
if type(c/(n-1),integer) then print(n); fi; od; end: P(10^9)

Mathematica

Select[Range[2, 10^7], Divisible[FromDigits@ Flatten@ Map[IntegerDigits, {#, # + 1}], # - 1] &] (* Michael De Vlieger, Jan 19 2017 *)

Formula

a(n) = A069860(n) + 1. - Alois P. Heinz, Jan 19 2017

Extensions

Two more terms (using A069860) from Alois P. Heinz, Jan 19 2017