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based on The Ehrenfeucht - Mycielski Sequence idea
Posted by: "Roger Bagula" rlbagulatftn at (no spam) yahoo.com rlbagulatftn
Fri Jun 20, 2008 4:15 pm (PDT)
It is probably more like a Cantor type of sequence: ( like the change
the end proof)
it takes the last iteration , doubles it and changes the last element:
A[0] = {0, 1, 0};
b[n_] := b[n] = Table[If[m < Length[
A[n - 1]], A[
n - 1][[m]],
If[A[n - 1][[Length[A[n - 1]]]] == 1, 0, 1]], {m, 1, Length[A[n -
1]]}]
A[n_] := A[n] = Flatten[Join[A[n - 1], b[n]]]
A[5]
{0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1,
0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0,
0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1,
0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0,
1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1}
The binary sums are: ( gets very large very fast)
Table[Sum[A[n][[m]]*2^(m - 1), {m, 1, Length[A[n]]}], {n, 0, 10}]
{2, 50, 1202, 13313202, 82620990563506, 62869822651806431913517458610,
1842509658606956899023055943058033268959392179964275795122,...
Straight one's sum is;
(*A001045 Jacobsthal sequence : a(n) = a(n - 1) + 2a(n - 2), with a(0) =
0, a(
1) = 1.
(Formerly M2482 N0983) *)
Table[Apply[Plus, A[n]], {n, 0, 10}]
{1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365}
I call it a semi-self-similar sequence.
Respectfully, Roger L. Bagula
11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814
:http://www.geocities.com/rlbagulatftn/Index.html
alternative email: rlbagula at (no spam) sbcglobal.net |
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