Re: Re:NestWhile

*To*: mathgroup at smc.vnet.net*Subject*: [mg23656] Re: Re:NestWhile*From*: "Paul R. Wellin" <wellin at wolfram.com>*Date*: Sun, 28 May 2000 23:09:07 -0400 (EDT)*References*: <8eg6sc$hd7@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Although slightly tangential to the initial thread here, I thought those who are interested in Keith numbers/sequences may like to search for them. Some time ago, I wrote a short program to do this. The first function KeithQ determines whether a number n is a Keith number in base b (base 10 by default, but it is interesting to look in other bases). The second simple function SearchKeith picks out all Keith numbers in a specified range. KeithQ[n_, b_:10] := Module[{t = IntegerDigits[n, b]}, While[Last[t] < n, t = Rest[Append[t, Plus @@ t]]]; Last[t] == n] SearchKeith[a_, b_] := Select[Range[a, b], KeithQ] Here are all the Keith numbers between 100 and 2000: In[3]:= SearchKeith[100, 2000] // Timing Out[3]= {2.58 Second, {197, 742, 1104, 1537}} Using the function below, you can check 742 for example: In[4]:= V3KeithSequence[742] Out[4]= {7, 4, 2, 13, 19, 34, 66, 119, 219, 404, 742} Paul Wellin Wolfram Research, Inc. wellin at wolfram.com "Alan W.Hopper" <awhopper at hermes.net.au> wrote in message news:8eg6sc$hd7 at smc.vnet.net... > > Dear mathgroup , > > > Concerning my query before Easter, about a version 3 equivalent to > NestWhile. > > Thanks to Hartmut Wolf, Daniel Reeves, Andrzej Kozlowski, and > Jens-Peer Kuska > for their solutions. > > And I received an e-mail from Eric Bynum of Wolfram Technical Support, > with code > which appropriately utilizes both Nest and While. Thanks also, Eric. > > > Here is Eric's Mathematica 3 Keith Sequence solution ; > > > In[1]:= > V3KeithSequence[n_Integer?Positive] := > Module[{d = IntegerDigits[n], l, counter, lis}, > l = Length[d]; > counter = 1; > While[Nest[Append[#, Plus @@ Take[#, -l]] &, d, counter][[-1]] < > n, > counter++; > lis = Nest[Append[#, Plus @@ Take[#, -l]] &, d, counter]]; > lis > ] > > In[5]:= > V3KeithSequence[197] > > Out[5]= > {1, 9, 7, 17, 33, 57, 107, 197} > > > Where as before, 1+9+7=17, 9+7+17=33, etc., ending again with 197. > > > > > Alan Hopper > > awhopper at hermes.net.au > > >