# No subject

murthy amarnath amarnath_murthy at yahoo.com
Wed Jun 2 16:11:28 CEST 2004

```Neil and seq fans,
what shape the following sequence would  finally take?
Rearrangement of natural numbers.
a(1) = 1 and let n = a(k) then  n+1= a(k-n-1) in case
a(k-n-1)is not occupied by some non zero number else
n+1 = a(k+n+1).

One can start building up the sequence like this:
Place zeros at locations which can not be decided in
that step and then replace them by nonzero numbers as
and when possible in further steps ;
first step: 1,0,2,0,0,3,...
in the second step the zero following 1 is replaced
by 4 etc.
--1,4,2,0,0,3,5,0,0,0,0,0,6,
--1,4,2,0,0,3,5,0,0,0,0,0,6,0,0,0,0,0,0,7,
--1,4,2,0,0,3,5,0,0,0,0,8,6,0,0,0,0,0,0,7
--1,4,2,0,0,3,5,0,0,0,0,8,6,0,0,0,0,0,0,7,9,
--1,4,2,0,0,3,5,0,0,0,10,8,6,0,0,0,0,0,0,7,9,
--1,4,2,0,0,3,5,0,0,0,10,8,6,0,0,0,0,0,0,7,9,11,
--1,4,2,0,0,3,5,0,0,12,10,8,6,0,0,0,0,0,0,7,9,11,
--1,4,2,0,0,3,5,0,0,12,10,8,6,0,0,0,0,0,0,7,9,11,13,
--1,4,2,0,0,3,5,0,14,12,10,8,6,0,0,0,0,0,0,7,9,11,13,
--1,4,2,0,0,3,5,0,14,12,10,8,6,0,0,0,0,0,0,7,9,11,13,15
--1,4,2,0,0,3,5,16,14,12,10,8,6,0,0,0,0,0,0,7,9,11,13,15
--1,4,2,0,0,3,5,16,14,12,10,8,6,0,0,0,0,0,0,7,9,11,13,15,17

--1,4,2,0,0,3,5,16,14,12,10,8,6,0,0,0,0,0,0,7,9,11,13,15,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,...

and so on
Conjecture:There will remain no zeros left finally.
Can some one please let me know what is a(4) and a(5).
thanks
regards
amarnath murthy

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