[seqfan] a(a(n)) is even <==> a(a(n)) is odd

[Eric Angelini]

Hello SeqFans,
http://www.research.att.com/~njas/sequences/A080653
If we drop here the "monotonically increasing sequence", we get:
n = 1,2,3,4,5, 6,7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,...
S = 2,4,5,6,8,10,9,12,16,14,13,18,24,22,17,20,32,26,21,34,40,30,42,28,...

The same here:
http://www.research.att.com/~njas/sequences/A079905
If we drop there the "monotonically increasing sequence", we get:
n = 1,2,3,4,5,6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,...
S = 1,3,5,6,7,9,11,10,13,17,15,14,19,25,23,18,21,33,27,22,35,41,31,26,...

(computed by hand -- this might be worth entering the database, I guess)
Best,
É.