A number    is a Friedman number if it can be obtained combining all its digits with the 5 arithmetic operations and concatenation (of digits, not of results).

For example,    is a Friedman number since it can be written as  .

M. Brand has proved that Friedman numbers have density 1, i.e., even if there are infinite numbers which are not Friedman (like all powers of 10), the probability that a number    is not Friedman asymptotically vanishes as    increases.

Many nice and interesting results about Friedman numbers are reported on the Erich Friedman web page linked below.

A Friedman number can be a repdigit, like

or a pandigital number, like

You can download a text file (Friedman_numbers_1e6.txt) containing a list of Friedman numbers up to    and their decompositions.

The first Friedman numbers are 25, 121, 125, 126, 127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024, 1206, 1255, 1260, 1285, 1296, 1395, 1435, 1503, 1530, 1792, 1827, 2048, 2187, 2349, 2500, 2501 more terms