[seqfan] A variant of A114055 (runs of equal parity digits alternate)

[Eric Angelini]

Hello SeqFans,

 

Here is A114055:

 

«Self-describing sequence : 

runs of equal parity digits alternate 

("0" is considered as an even digit); 

the length of each run is given by the sequence itself.»

 

http://www.research.att.com/~njas/sequences/A114055

 

Let us drop the (not mentioned) constraint that a(n-1)<a(n)

and replace the definition by:

 

"Always take the smallest available integer not yet in

 the sequence such that runs of equal parity digits

 alternate ("0" is considered as an even digit) 

 and such that the length of each run is given by the

 sequence itself."

 

We would then have (I think) this permutation of N:

 

S=1,2,4,3,5,7,9,6,8,21,11,13,20,22,24,21,15,17,19,31,28,40,42,...

  o e e o o o o e e eo oo oo ee ee ee eo oo oo oo oo ee ee ee

  1  2     4      3     5        7           9          6 <-- this is S

 

Best,

É.