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G.f.: 1/(1-x) * Sum_{k>=0} (2^(-1+2^k))*x^2^k/(1+x^2^k). - John Tyler Rascoe, May 22 2024
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Numbers These are numbers whose binary indices are all powers of 2, where a binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, the terms together with their binary expansions and binary indices begin:
From Gus Wiseman, Dec 29 2023: (Start)
Numbers whose binary indices are all powers of 2, where a binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, the terms together with their binary expansions and binary indices begin:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
8: 1000 ~ {4}
9: 1001 ~ {1,4}
10: 1010 ~ {2,4}
11: 1011 ~ {1,2,4}
128: 10000000 ~ {8}
129: 10000001 ~ {1,8}
130: 10000010 ~ {2,8}
131: 10000011 ~ {1,2,8}
136: 10001000 ~ {4,8}
137: 10001001 ~ {1,4,8}
138: 10001010 ~ {2,4,8}
139: 10001011 ~ {1,2,4,8}
For powers of 3 we have A368531.
(End)
a(2^n+1) = 2^(2^n-1) = A058891(n+1). - Gus Wiseman, Dec 29 2023
a(2^n) = A072639(n). - Gus Wiseman, Dec 29 2023
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a:= n-> (l-> add(l[i+1]*2^(2^i-1), i=0..nops(l)-1)/2)(Bits[Split](n-1)):
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