A342157 Base-10 numbers m such that k*m = d||d||...||d (here || appears k-1 times), where k is the length of m, d is any m's digit and || represents concatenation.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 148, 185, 148148

Offset

1,3

Comments

All numbers satisfying such conditions must be smaller than 10^9, because if we take any 10-digit number m, 10m is an 11-digit number while d||d||...||d is a 10-digit number.

148 and 148148 are the only numbers in the sequence for which d is not necessarily the last digit (for 148 we take d=4, which is the second digit of 148 and for 148148 we take d=8, which is the last, but also the third digit).

Links

Table of n, a(n) for n=1..13.

Example

m=148 is in the sequence, because if we multiply 148 by k=3 (length of 148) we obtain 444, which is d||d||d for d=4 (second digit of 148)

Prog

(C++)
#include <iostream>
#include <math.h>
using namespace std;
int length(int a){for(int i=0; i<=10; i++){if(pow(10, i)<=a && pow(10, i+1)>a){return i+1; }}}
int DC(int a, int b){int c=(a%(int)(pow(10, b))-a%(int)(pow(10, b-1)))/(int)(pow(10, b-1)); int l=length(a); int s=0; for(int i=0; i<l; i++){s=s+(int)(pow(10, i)); }return s*c; }
int main() {for(int n=1; n<pow(10, 9); n++){int k=length(n); for(int i=1; i<=k; i++){if(k*n==DC(n, i)){cout<<n<<endl; }}}}

Crossrefs

Sequence in context: A001104 A151544 A032561 * A306360 A023052 A005188

Adjacent sequences: A342154 A342155 A342156 * A342158 A342159 A342160

Keyword

nonn,base,fini,full

Author

Andrzej Kukla, Mar 02 2021

Status

approved