Friedman Number/Examples

Examples of Friedman Numbers

The first few base $10$ Friedman numbers are as follows:

\(\ds 25\)

\(=\)

\(\ds 5^2\)

\(\ds 121\)

\(=\)

\(\ds 11^2\)

\(\ds 125\)

\(=\)

\(\ds 5^{\paren {1 + 2} }\)

\(\ds 126\)

\(=\)

\(\ds 21 \times 6\)

\(\ds 127\)

\(=\)

\(\ds 2^7 − 1\)

\(\ds 128\)

\(=\)

\(\ds 2^{\paren {8 - 1} }\)

\(\ds 153\)

\(=\)

\(\ds 51 \times 3\)

This sequence is A036057 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).