Friedman Numbers

This collection was established on 15 July 2009 after a nBAB for the number 128 was posted.

       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, 
     2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 
     2592, 2737, 2916, 3125, 3159, 3281, 3375, 3378, 
     3685, 3784, 3864, 3972, 4088, 4096, 4106, 4167, 
     4536, 4624, 4628, 5120, 5776, 5832, 6144, 6145, 
     6455, 6880, 7928, 8092, 8192, 9025, 9216, 9261,
     ...

From OEIS.org: "Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results)." {OEIS.org::id:A036057}

Note: A nice Friedman number has a math expression in which the digits are used in the order in which they are found in the number.

Update::2009.07.18

MathBabbler spent some time finding math expressions for some of the Friedman numbers.

     25 = 5^2
    121 = 11^2
    125 = 5^(2+1)
    126 = 21 * 6
    127 = 2^7 - 1
    128 = 2^(8 - 1)
    153 = 51 * 3
    216 = 6^3
    289 = 17^2
    343 = (3 + 4)^3    [nice]
    625 = 5^(6 - 2)
    688 = 86 * 8
    736 = 7 * 3^6      [nice]
   1022 = 2^10 - 2
   1024 = (4 - 2)^10
   ....
   2048 = 8^4 / 2 + 0
   2187 = 27 * 81
   2349 = 29 * 3^4
   2500 = 50^2 + 0
   2501 = 50^2 + 1
   2502 = 50^2 + 2
   ....

Note: Writing a computer program to determine if a number is a Friedman number is non-trivial (i.e. MathBabbler thinks it is hard).


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 15 July 2009
+ added 32 on 13 June 2009
+ added 128 on 15 July 2009
+ added 2500 on 25 July 2009
+ added 4096 on 30 December 2009
+ added 1024 on 30 December 2009
+ added 8192 on 03 March 2010
+ added 343 on 19 March 2010
+ added 3125 on 05 September 2011
+ added 347 on 13 December 2013
+ added 1296 on 26 February 2015
+ added 289 on 16 October 2015

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This work is licensed under a Creative Commons Attribution 3.0 United States License.