NestWhile
- To: mathgroup at smc.vnet.net
- Subject: [mg23039] NestWhile
- From: "Alan W.Hopper" <awhopper at hermes.net.au>
- Date: Thu, 13 Apr 2000 02:43:25 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Others like myself who are still using Mathematica 3, may have been
interested to see that the new cryptic @@@ function can be programmed
into a user function for version 3, as explained by Hartmut Wolf and
Daniel Reeves.
But I have a query to pose about another new version 4 function ,
that is NestWhile, which I assume can also be approximated in version
3.0.
This code was taken from Eric Weisstein's IntegerSequences.m package,
obtained from the mathworld.wolfram site ;
KeithNumberQ[n_Integer?Positive]:=(KeithSequence[n][[-1]] == n)
KeithSequence[n_Integer?Positive]:= Module[{d = IntegerDigits[n], l},
l = Length[d];
NestWhile[Append[#, Plus @@ Take[#,-l]] &, d, #[[-1]] < n &]
]
The first Keith Number is 197 and it's Keith Sequence should be
{1, 9, 7, 17, 33, 57, 107, 197}, or similar.
as starting with the digits of 197 ,
1 + 9 + 7 = 17
9 + 7 + 17 = 33
7 + 17 + 33 = 57
17 + 33 + 57 = 107
33 + 57 + 107 = 197
Other small Keith Numbers are 742, 1104, 1537, 2208,
a large one is 97295849958669 .
(see Don Piele - Mathematica Pearls - Mathematica in Research and
Education - Vol 6 No 3 , p 50, also Vol 7 No 1, p 45.
So the question is how can a Mathematica 3 version of NestWhile be
substituted into the above code?
Alan Hopper
awhopper at hermes.net.au
- Follow-Ups:
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- From: Hartmut Wolf <hwolf@debis.com>
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