
COMMENTS

Binary expansion of n does not contain 1bits at even positions.
Integers whose base4 representation consists of only 0's and 2's.
a(n)=2 A000695(n). Every nonnegative even number is a unique sum of the form a(k)+2a(l); moreover, this sequence is unique with such property. [Vladimir Shevelev, Nov 07 2008]
Also numbers such that the digital sum base 2 and the digital sum base 4 are in a ratio of 2:4.  Michel Marcus, Sep 23 2013
From Gus Wiseman, Jun 10 2020: (Start)
Numbers k such that the kth composition in standard order has all even parts. The kth composition in standard order (graded reverselexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. For example, the sequence of all compositions into even parts begins:
0: () 520: (6,4) 2080: (6,6)
2: (2) 522: (6,2,2) 2082: (6,4,2)
8: (4) 544: (4,6) 2088: (6,2,4)
10: (2,2) 546: (4,4,2) 2090: (6,2,2,2)
32: (6) 552: (4,2,4) 2176: (4,8)
34: (4,2) 554: (4,2,2,2) 2178: (4,6,2)
40: (2,4) 640: (2,8) 2184: (4,4,4)
42: (2,2,2) 642: (2,6,2) 2186: (4,4,2,2)
128: (8) 648: (2,4,4) 2208: (4,2,6)
130: (6,2) 650: (2,4,2,2) 2210: (4,2,4,2)
136: (4,4) 672: (2,2,6) 2216: (4,2,2,4)
138: (4,2,2) 674: (2,2,4,2) 2218: (4,2,2,2,2)
160: (2,6) 680: (2,2,2,4) 2560: (2,10)
162: (2,4,2) 682: (2,2,2,2,2) 2562: (2,8,2)
168: (2,2,4) 2048: (12) 2568: (2,6,4)
170: (2,2,2,2) 2050: (10,2) 2570: (2,6,2,2)
512: (10) 2056: (8,4) 2592: (2,4,6)
514: (8,2) 2058: (8,2,2) 2594: (2,4,4,2)
(End)
