Re:NestWhile

• To: mathgroup at smc.vnet.net
• Subject: [mg23265] Re:NestWhile
• From: "Alan W.Hopper" <awhopper at hermes.net.au>
• Date: Sat, 29 Apr 2000 22:05:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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

```

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