[seqfan] Another phenomenon?

[Vladimir Shevelev]

Dear SeqFans,
 
By Moser-Newman phenomenon, among the first N positive integers multiple of 3, the evil numbers (A001969) are always in the majority. But what is happened, if to remove from the positive numbers the multiples of 3? Then for multiples of 5,we have always in the majority neither evil nor odious numbers. For example, among the first 28 such numbers, there are 15 odious ones. On the other hand, by our observations, we conjecture that we have another phenomenon: among the first N such positive integers multiple of 7, the odious numbers (A000069) are always in the majority. 
Maybe, such a phenomenon already is known? Concerning it,I submitted A229826.
It is interesting also to observe, for a fixed odd odious number r, r=11,13,19,25,..., is there a close phenomenon on such numbers nultiple of r.
 
Best regards,
Vladimir

 Shevelev Vladimir‎