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COMMENTS
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Binary expansion of n does not contain 1-bits at even positions.
Integers whose base-4 representation consists of only 0's and 2's.
Every nonnegative even number is a unique sum of the form a(k)+2*a(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
Numbers k such that the k-th composition in standard order has all even parts. The k-th composition in standard order (graded reverse-lexicographic, 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)
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