[seqfan] Re: A057652 has no more terms below 10^6
Alonso Del Arte
alonso.delarte at gmail.com
Thu Oct 21 01:11:55 CEST 2010
Using Tony's modification of Robert's code but with my own LuckableQ
function, I have verified that there are no more terms up to 10^6 in about 4
minutes. I'm guesstimating verification up to 10^7 would take 40 minutes,
but that'll have to be another day for me. I should be preparing for the
Music of Engineering event this Friday.
I don't know if anyone has studied the equivalent of Gilbreath's conjecture
for lucky numbers, but it appears that instead of a line of 1s, you get a
line of alternating 2s and 0s, but there can be two or three consecutive 2s
or 0s in a row. I haven't been able to discern any pattern to this
alternation.
Al
On Wed, Oct 20, 2010 at 2:03 PM, T. D. Noe <noe at sspectra.com> wrote:
> I tend to agree with the conjecture that there are no additional terms.
> However, it's always fun to look.
>
> Using Mathematica, it takes only about an hour to verify that there are no
> additional terms less than 10^7. Here is the code to create the lucky
> numbers (modified from Robert Wilson's code):
>
> nn=10^7;
> lucky=Range[1,nn,2];
> sieve[n_Integer]:=Module[{k=lucky[[n]]},
> lucky=Delete[lucky,Table[{i},{i,k,Length[lucky],k}]]];
> n=1; While[lucky[[n]] < Length[lucky], n++; sieve[n]]
>
> Using the BinarySearch function in the Combinatoria package, the following
> function quickly determines whether n is lucky:
>
> LuckyQ[n_Integer] := IntegerQ[BinarySearch[lucky,n]]
>
> This tests n up to 10^7:
>
> Do[k=2; While[k<n && LuckyQ[n-k], k=2k]; If[k=>n, Print[n]], {n,nn}]
>
> Best regards,
>
> Tony
>
>
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