Editing Friedman number (section)

==Results in base 10==
The expressions of the first few Friedman numbers are:

{|class="wikitable"
|number
|expression
|number
|expression
|number
|expression
|number
|expression
|-
|25
|5<sup>2</sup>
|127
|2<sup>7</sup>−1
|289
|(8+9)<sup>2</sup>
|688
|8×86
|-
|121
|11<sup>2</sup>
|128
|2<sup>(8−1)</sup>
|343
|(3+4)<sup>3</sup>
|736
|3<sup>6</sup>+7
|-
|125
|5<sup>(1+2)</sup>
|153
|3×51
|347
|7<sup>3</sup>+4
|1022
|2<sup>10</sup>−2
|-
|126
|6×21
|216
|6<sup>(2+1)</sup>
|625
|5<sup>(6−2)</sup>
|1024
|(4−2)<sup>10</sup>
|}

A '''nice''' Friedman number is a Friedman number where the digits in the expression can be arranged to be in the same order as in the number itself. For example, we can arrange 127 = 2<sup>7</sup> − 1 as 127 = −1 + 2<sup>7</sup>. The first nice Friedman numbers are:

:127, 343, 736, 1285, 2187, 2502, 2592, 2737, 3125, 3685, 3864, 3972, 4096, 6455, 11264, 11664, 12850, 13825, 14641, 15552, 15585, 15612, 15613, 15617, 15618, 15621, 15622, 15623, 15624, 15626, 15632, 15633, 15642, 15645, 15655, 15656, 15662, 15667, 15688, 16377, 16384, 16447, 16875, 17536, 18432, 19453, 19683, 19739 {{OEIS|id=A080035}}.

A '''nice''' Friedman prime is a '''nice''' Friedman number that's also prime. The first nice Friedman primes are:

:127, 15667, 16447, 19739, 28559, 32771, 39343, 46633, 46663, 117619, 117643, 117763, 125003, 131071, 137791, 147419, 156253, 156257, 156259, 229373, 248839, 262139, 262147, 279967, 294829, 295247, 326617, 466553, 466561, 466567, 585643, 592763, 649529, 728993, 759359, 786433, 937577 {{OEIS|id=A252483}}.

Michael Brand proved that the density of Friedman numbers among the naturals is 1,<ref>Michael Brand, "Friedman numbers have density 1", ''Discrete Applied Mathematics'', '''161'''(16–17), Nov. 2013, pp. 2389-2395.</ref> which is to say that the probability of a number chosen randomly and uniformly between 1 and ''n'' to be a Friedman number tends to 1 as ''n'' tends to infinity. This result extends to Friedman numbers under any base of representation. He also proved that the same is true also for binary, ternary and quaternary nice Friedman numbers.<ref>Michael Brand, "On the Density of Nice Friedmans", Oct 2013, https://arxiv.org/abs/1310.2390.</ref> The case of base-10 nice Friedman numbers is still open.

[[Vampire number]]s are a subset of Friedman numbers where the only operation is a multiplication of two numbers with the same number of digits, for example 1260 = 21 × 60.