A357482 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1).
0, 1, 2, 3, 7, 4, 5, 63, 8, 6, 9, 16, 127, 11, 10, 12, 13, 14, 19, 511, 1023, 15, 21, 17, 31, 18, 20, 22, 24, 25, 33, 23, 27, 26, 28, 35, 37, 38, 41, 1535, 29, 30, 32, 34, 47, 36, 40, 55, 39, 43, 42, 45, 255, 46, 51, 383, 48, 44, 4095, 64, 447, 65, 95, 53, 191, 767, 1791, 59, 49, 54, 57, 50, 52
Offset: 0
Examples
a(7) = 63 as 63 = 111111_2 which contains six 1's, the concatenation of the binary values of a(0)..a(6) is "011011111100101" which contains ten 1's, and 6 + 10 = 16 = 10000_2 which does not appear in the concatenated binary string of previous terms. All smaller unused numbers less than 63 have one to five 1's in their binary values leading to sums of 11, 12, 13, 14 or 15, but the binary values of these five sums all appear in the concatenated binary string of previous terms.
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