A281233 - OEIS

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, 5000000002, 14285714287, 16666666668

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OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..35.

FORMULA

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

EXAMPLE

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

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 *)