World!Of
Numbers

WON plate
70 |

[ December 27, 1999 ]
Find more smallest Squares and Cubes whose digits
occur a same number of times

E.g. 100112 = 100220121 has exactly three zero's, three ones and three two's !
Note that the number of different digits in the decimal expansion
may differ from their required frequency.
The next table already give the solutions for frequencies 1 to 7 for the squares.
Though the numbers are definitely 'base-related' they surely display a notable beauty !

Some questions I would like to ask are for instance :
Are there always solutions possible for any frequency ?
What are the possible shortcuts one can make while programming this puzzle ?

FrequencySquare RootSquare
100
2887744
310.011100220121
431.646.1911001481404808481
516.431.563
3.180.566.996
269996262622969
10116006416044464016 is next one
6667.567.716445646655445456656
by Jeff Heleen [ January 17, 2000 ]
710.715.008.859114811414848448481881
by Jeff Heleen [ January 20, 2000 ]
8??
9??
10??

For the Cubes and higher Powers solutions
The title is Numbers whose digits occur with same frequency.

A000070 Prime Curios! Prime Puzzle
Wikipedia 70 Le Nombre 70 Numberland 70
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