[seqfan] Re: Underline a(n) when n=3k

M. F. Hasler seqfan at hasler.fr
Sat Mar 7 20:53:22 CET 2015


On Thu, Mar 5, 2015 at 2:27 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:

> Hello SeqFans,
>
> S =
> 1,2,1,1,1,2,1,2,1,1,2,1,1,1,1,2,1,2,1,1,1,1,2,2,1,2,1,1,1,1,1,1,2,2,2,1,1,2,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,1,1,2,2,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,...
>
> Underline a(n) when n=3k (k = 1-->oo).
> The underlined terms reproduce S.
> The non underlined terms reproduce S too.
>

This is actually the m=3 version of the m=10 variant A126616
<https://oeis.org/A126616>.
The other variants with general definition:
"a(n) = n for n < m; a(mn) = a(n); if every m-th term (a(m), a(2m),
a(3m),...) is deleted, this gives back the original sequence"
are (now) A255824 - A255829 (thanks to Neil for speedy publication ^^).

The list of indices of 2's in Eric's above (m=3) sequence
(or: indices of nonzero terms in [the (1,2) -> (0,1) variant] A117943)
is A178931,
Otherwise said, A117943 is the characteristic function of A178931.
It is interesting that the latter is constructed from a quite different
approach.

One might consider as more natural the "0-based" versions of the m=3..10
family
(not only for values but also for indices, i.e., a(n)=n for n=0..m-1,...)
but it is probably too much to add these "almost duplicates" to OEIS.

 --
Maximilian


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