
COMMENTS

In other words, numbers whose binary representation consists of one or more repeating blocks with only one 1 in each block.
Also, fixed points of the permutations A139706 and A139708.
Each a(n) is a term of A064896 multiplied by some power of 2. As such, this sequence must also be a subsequence of A125121.
Also the numbers that uniquely index a Haar graph (i.e., 5 and 6 are not in the sequence since H(5) is isomorphic to H(6)).  Eric W. Weisstein, Aug 19 2017
From Gus Wiseman, Apr 04 2020: (Start)
The kth composition in standard order (row k of 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. This gives a bijective correspondence between nonnegative integers and integer compositions. This sequence lists all positive integers k such that the kth composition in standard order is constant. For example, the sequence together with the corresponding constant compositions begins:
0: () 136: (4,4)
1: (1) 170: (2,2,2,2)
2: (2) 255: (1,1,1,1,1,1,1,1)
3: (1,1) 256: (9)
4: (3) 292: (3,3,3)
7: (1,1,1) 511: (1,1,1,1,1,1,1,1,1)
8: (4) 512: (10)
10: (2,2) 528: (5,5)
15: (1,1,1,1) 682: (2,2,2,2,2)
16: (5) 1023: (1,1,1,1,1,1,1,1,1,1)
31: (1,1,1,1,1) 1024: (11)
32: (6) 2047: (1,1,1,1,1,1,1,1,1,1,1)
36: (3,3) 2048: (12)
42: (2,2,2) 2080: (6,6)
63: (1,1,1,1,1,1) 2184: (4,4,4)
64: (7) 2340: (3,3,3,3)
127: (1,1,1,1,1,1,1) 2730: (2,2,2,2,2,2)
128: (8) 4095: (1,1,1,1,1,1,1,1,1,1,1,1)
(End)
