[seqfan] Re: Sum of all valid substrings (VS)
Marc LeBrun
mlb at well.com
Sun Jan 18 20:43:06 CET 2009
>=Eric Angelini
> Let's try to build another sequence, slightly changing this:
> into a(n) = a(n-1) + sum of [set of proper] substrings of a(n-1)
With apologies for making suggestions I don't have time to pursue
myself, would anyone be willing to look into this (and variants) in
binary (which some may agree are generally more interesting than decimal)?
In binary the sets of substrings are given in A119709, their
cardinality in A078822, sum in A078823. The analogs for proper
substrings, A078822(n)-1 and A078823(n)-n, aren't in the OEIS, nor is
the XOR of the full set (ie including n) 1,3,2,7,6,6,5,... etc
(Iteration of this last may also produce some interesting seqs).
There should also be some cross-refs linking the binary and decimal cliques.
Best regards,
--MLB
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