A328379 a(n) is the sum of the distinct numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
0, 1, 3, 4, 7, 11, 12, 11, 15, 24, 31, 29, 28, 37, 33, 26, 31, 49, 66, 61, 71, 92, 85, 67, 60, 87, 103, 90, 77, 95, 78, 57, 63, 98, 133, 121, 150, 191, 177, 138, 151, 215, 254, 219, 197, 240, 199, 145, 124, 185, 237, 210, 235, 293, 262, 199, 165, 230, 263, 223
Offset: 0
Examples
The first terms, alongside the binary representations of n as well as those of the numbers that appear in it, are:
n a(n) bin(n) {bin(s)}
-- ---- ------ ----------------------------
0 0 0 {0}
1 1 1 {1}
2 3 10 {0, 1, 10}
3 4 11 {1, 11}
4 7 100 {0, 1, 10, 100}
5 11 101 {0, 1, 10, 11, 101}
6 12 110 {0, 1, 10, 11, 110}
7 11 111 {1, 11, 111}
8 15 1000 {0, 1, 10, 100, 1000}
9 24 1001 {0, 1, 10, 11, 100, 101, 1001}
10 31 1010 {0, 1, 10, 11, 100, 101, 110, 1010}
Links
Programs
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PARI
a(n, base=2) = { my (b=digits(n, base), s=[0]); for (k=1, #b, s = setunion(s, apply(o -> base*o+b[k], s))); vecsum(s) }