Goodstein expansion

• To: mathgroup at smc.vnet.net
• Subject: [mg132315] Goodstein expansion
• From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
• Date: Sat, 8 Feb 2014 04:02:30 -0500 (EST)
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```The Goodstein expansion of integers  (see for instance  Stillwell," Roads to Infinity", pag.47)

Given an integer n we can write it as sum of powers of  2

87=2^6+2^4+2^2+1=2^(2^2+2)+2^(2^2)+2^2+2^0

More generally assuming an integer b as a base, we can write  n as a sum of power of b with coefficients <b
es.:  b=5

87=3*5^2+2*5^1+2*5^0.

I can do it by means of a long and obvious routine with lots  of  If[]  and While[].
May be someone can do it by means of the recursive properties of Mathematica language?
Many thanks to all the friends of this group!
Roberto

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