OFFSET
0,2
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.
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
AUTHOR
Scott R. Shannon, Jan 16 2023
STATUS
approved