A359858 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the ones' complement of the binary string of a(n-1) + a(n) does not appear in the binary string concatenation of a(0)..a(n-1).

0, 2, 6, 5, 3, 8, 14, 18, 20, 12, 24, 23, 9, 27, 37, 10, 22, 25, 7, 40, 39, 52, 42, 49, 15, 32, 59, 35, 56, 38, 53, 41, 50, 44, 47, 81, 13, 78, 16, 75, 57, 34, 94, 61, 30, 98, 60, 31, 97, 58, 33, 122, 63, 28, 127, 55, 36, 126, 65, 118, 67, 95, 88, 74, 109, 76, 86, 99, 84, 101, 82, 80, 103, 187

Offset: 0

Author

Scott R. Shannon, Jan 16 2023

Keywords

• nonn
• base
• look

Comments

In the first 100000 terms the fixed points are 55, 123, 1779, 2009, although it is likely more exist. The sequence is conjectured to be a permutation of the positive integers. Note that 1 does not appear until the 160th term.

Examples

			a(3) = 5 as the concatenation of a(0)..a(2) in binary is "010110" and a(2) + 5 = 6 + 5 = 11 = 1011_2 whose ones' complement = 100_2, which does not appear in the concatenated string. Note the ones' complements of 6+1, 6+3, 6+4 are 0_2, 110_2, 101_2, all of which appear in the concatenated string.
		

Links

• Scott R. Shannon, Image of the first 50000 terms. The green line is a(n) = n. Note some of the patterns appearing are reminiscent of those in the images of A357082.

Crossrefs

Cf. A035327, A007088, A357082, A355611.