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JT
Posts:
1,388
Registered:
4/7/12


Numbersystems using powers
Posted:
Sep 20, 2013 1:15 AM


Is there notational signs other then for square, cubic, quarctic and so on?
We could make numbersystems raised to powers and even mixed for real big numbers, what is thse called?
^2 8 4 +3 = 64+16+3 = 83
^3 4 2 +11 = 64+8+11=83
^4 3 +2 = 81+2 = 83
Even mixes like ^5 2 2 ^2 +3 or ^5 2 2 2 13 = 83
Is there a formula for writing the shortest notation on powers for really big numbers or maybe an algorithm.
If numbers were written this way could one take shortcuts to certain arithmetic operations or would the work be same or even bigger?
I do not know how mathematicians and computers do operations on really big numbers, i think i could implement functions for doing these type of arithmetic operations but they are probably already worked out?
How is the computional cost doing this arithmetic vs using power towers arithmetic, and digit sizes vs powertowers? What is the benefits drawbacks?
Is the shortest way to write a big number number is having as many digits in the base as in the power?
If we take a big none repetive number what is the shortest way to date to write this.
1294956383736345003882734533454692924556654929227373232843737939272746283284811232344958373489393922203048937348556341
Let see who can come up with the shortest way to write it using decimals and two additional signs. Preferably you should be able to arithmetic in an easy way albeit not the standard way. So no compression like solutions.
Well wolfram did not write any short form. http://www.wolframalpha.com/input/?i=+1294956383736345003882734533454692924556654929227373232843737939272746283284811232344958373489393922203048937348556341



