[seqfan] Self-describing chunks of primes
Eric Angelini
Eric.Angelini at kntv.be
Sat Nov 30 18:28:37 CET 2013
Hello SeqFans,
We want the first permutation of the
integers >0 describing its chunks
of primes (separated by non-primes):
S=1,2,4,3,5,6,7,11,13,17,8,19,23,29,9,31,37,41,43,47,10,53,...
If we mark the non-primes of S we get:
S=(1),2,(4),3,5,(6),7,11,13,17,(8),19,23,29,(9),31,37,41,43,47,(10),53,...
And if we make the count of the non-
marked integers we get successively:
1 integer [the "2"]
2 integers ["3" and "5"]
4 integers ["7,11,13,17"]
3 integers["19,23,29"]
5 integers ["31,37,41,43,47"]
etc. -- said integers being the primes
in their natural order, marked integers
being the non-primes in their natural
order and the first column above being
the sequence S itself.
-------
The equivalent T seq where the roles are
reversed seems to start like this:
T=2,1,4,3,6,5,8,9,10,12,7,14,15,16,11,18,20,21,22,24,25,13,26,27,28,30,32,17,33,...
Marking the primes:
T=(2),1,4,(3),6,(5),8,9,10,12,(7),14,15,16,(11),18,20,21,22,24,25,(13),26,27,28,30,32,(17),33,...
Computing the size of each "non-prime chunk" gives:
2-1-4-3-6-5...
... which is T itself.
None of those seq are in the OEIS, I think.
Best,
É.
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