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

Author

Andrzej Kukla, Mar 02 2021

Keywords

• nonn
• base
• fini
• full

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).

Examples

			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)