do you know another Magic Square with this property? with the repeating digits of $\frac{1}{19} = 0.052631578947368421$ we can construct an exceptional magic square : > The number 19 is a cyclic number with a period of 18 before the digits start to repeat. > > The full term decimal expansion of the prime number 19 when multiplied by the values 1 to 18, may be arranged in a simple magic square of order-18, if the decimal point is ignored. All 18 rows, columns and the two main diagonals sum to the same value. S = 81. Of course this is not a pure magic square because a consecutive series of numbers from 1 to n is not used example of order 18 (Moved to an answer. The link died.) Are there **other numbers as well _19 and 383_** that can be used for making magic squares in such way ? **is it proved that in base 10 only _19 and 383_ have this property ? , what is for higher orders ?**

The numbers that work are tabulated at the Online Encyclopedia of Integer Sequences, where some references to the literature are given.