[seqfan] idea for a sequence

David Newman davidsnewman at gmail.com
Wed Oct 3 22:03:12 CEST 2012


Begin with the Van Der Korput sequence  a1=1/2, a2=1/4, a3=3/4,  a4=1/8,
a5=5/8, a6=3/8, a7=7/8,...

Now look at the place that  ak occupies in the sequence consisting of the
first k elements of the initial sequence when arranged in ascending order.
For example a1 occupies the first place in the subsequence consisting of
just a1.  a2 occupies the first place in the sequence 1/4, 1/2.  a3
occupies the third spot in the sequence 1/4, 1/2, 3/4.  a4 occupies the
first place in 1/8, 1/4, 1/2, 3/4.  a5 is in the fourth place in 1/8, 1/4,
1/2, 5/8, 3/4.

This gives the new sequence beginning, I believe, with 1, 1, 3, 1, 4, 3, 7,
1, 6, 4, 10, 3, 10, 7, 15,...

This does not seem to be in the OEIS.

I am away from my computer so I can't check this with Mathematica as I
ordinarily would.

Could someone check this please?  Add terms and submit it?

Other initial sequences can give the same derived sequence.



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