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0, 3, 2, 15, 0, 11, 6, 63, 0, 3, 10, 47, 8, 27, 14, 255, 0, 3, 2, 15, 0, 43, 22, 191, 0, 35, 10, 111, 24, 59, 30, 1023, 0, 3, 2, 15, 0, 11, 38, 63, 0, 3, 42, 175, 8, 91, 46, 767, 0, 3, 2, 143, 32, 43, 54, 447, 32, 99, 42, 239, 56, 123, 62, 4095, 0, 3, 2, 15, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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For any n >= 0:
- let s(n) be the unique finite set of nonnegative integers such that n = Sum_{e in s(n)} 2^e,
- then s(a(n)) corresponds to the set of nonnegative integers that are not the sum of two nonnegative integers not in s(n).
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LINKS
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FORMULA
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a(2^n-1) = 4^n-1.
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EXAMPLE
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The first terms, alongside the corresponding sets, are:
n a(n) s(n) s(a(n))
-- ---- ------------ ------------------------
0 0 {} {}
1 3 {0} {0, 1}
2 2 {1} {1}
3 15 {0, 1} {0, 1, 2, 3}
4 0 {2} {}
5 11 {0, 2} {0, 1, 3}
6 6 {1, 2} {1, 2}
7 63 {0, 1, 2} {0, 1, 2, 3, 4, 5}
8 0 {3} {}
9 3 {0, 3} {0, 1}
10 10 {1, 3} {1, 3}
11 47 {0, 1, 3} {0, 1, 2, 3, 5}
12 8 {2, 3} {3}
13 27 {0, 2, 3} {0, 1, 3, 4}
14 14 {1, 2, 3} {1, 2, 3}
15 255 {0, 1, 2, 3} {0, 1, 2, 3, 4, 5, 6, 7}
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PROG
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(PARI) a(n) = { my (v=0); for (x=0, 2*#binary(n), my (f=0); for (y=0, x, if (!bittest(n, y) && !bittest(n, x-y), f=1; break)); if (!f, v+=2^x)); return (v) }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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