subsidiary sequences in OEIS

[murthy amarnath]

Dear Neil and Seq fans,
I would like to suggest some derived sequences/
classification of sequencces from the OEIS some of
which i had perhaps mentioned earlier.

(1)This one applies to sequences which are
rearrangements of a particular type of numbers.
say rearrangement of natural numbers or prime numbers
etc.
A subsidiary sequence can be (defined) obtained  as
the  sequence of numbers m such that every eligible
member r less than m occurs earlier i.e.Index(r) <
index(m).
And one can explore whether these are finite or not.
(2) 
(i)Sequences such that every natural number is the sum
of a few terms.
e.g.  a(n) = 2^n etc.
(ii) Sequences such that every natural number is the
sum of atmost r terms.

(3) Sum of the reciprocals of the terms  of the
sequence is finite and whether the sum is equal to a 
fascinating  known constant.
thanks
sequentially
amarnath murthy

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