[seqfan] Connection between A182214 and A306399

[Ali Sada]

Hi Everyone,

If we add each two consecutive terms of A306399 we get

2,3,4,4,5,4,4,5,4,7,6,5,8,6,4,9,8,6,7,4,11,10,7,12,8,4,13,12,8,9,4,15,14,9,16,10,4,17,16,10,11,4,19,18,11,20,12,4,21,20,12,13,4,23,22,13,24,14,4,25,24,14,15,4,27,26,15,28,16,4,29,28,16,17,4,31,30,17,32,18,4,3 

This sequence is odd when n is:
2,5,8,10,12,16,19,21,23,27,30,32,34,38,41,43,45,49,52,54,56,60,63,65,67,71,74,76,78,82,85,87,89,93,96,98,100,104,107,109,111,115,118,120,122,126,129,131,133,137,140,142,144,148,151,153,155,159,162,164,166,170,173,175,177,181,184,186,188,192,195,197,199

 
The differences between these n's are:

3,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2

Except for the first term, this is A182214.

 
This was true for the first 1,000 terms of A306399. Will this connection continue? And why?

 

I would really appreciate your feedback.

 

Best,

 

Ali