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 A188215 Starting with an empty list, n is inserted after the a(n)th element such that the binary representations of the list's elements are always sorted lexicographically. 2
 0, 1, 2, 3, 3, 4, 6, 7, 4, 5, 7, 8, 11, 12, 14, 15, 5, 6, 8, 9, 12, 13, 15, 16, 20, 21, 23, 24, 27, 28, 30, 31, 6, 7, 9, 10, 13, 14, 16, 17, 21, 22, 24, 25, 28, 29, 31, 32, 37, 38, 40, 41, 44, 45, 47, 48, 52, 53, 55 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The last occurrence of any positive n in this sequence is a(2^(n - 1)). As the list in question expands, its initial terms converge toward A131577. The last item of the list is always zero or an element of A075427. LINKS T. D. Noe, Table of n, a(n) for n = 0..1023 FORMULA a(2^n + b) = n + b + 1 for b = 0 or 1. a(2^n - b) = 2^n - b for b = 1 or 2. EXAMPLE For example, an a(n) of 3 means that n should be inserted after the 3rd element of the list to keep the elements lexicographically ordered. [] (Initial empty list) [0] (Zero inserted at the beginning: a(0) = 0) [0, 1] (One inserted after element 1: a(1) = 1) [0, 1, 10] (Two inserted after element 2: a(2) = 2) [0, 1, 10, 11] (Three inserted after element 3: a(3) = 3) [0, 1, 10, 100, 11] (Four inserted after element 3: a(4) = 3) MATHEMATICA lst = {}; Table[s = IntegerString[n, 2]; lst = Sort[Append[lst, s]]; Position[lst, s][[1, 1]] - 1, {n, 0, 63}] (* T. D. Noe, Apr 19 2011 *) PROG (Python) l = [] for i in range(17): b = bin(i)[2:] l.append(b) l.sort() print(l.index(b)) CROSSREFS Cf. A264596. Sequence in context: A181692 A145806 A100989 * A162627 A023158 A120882 Adjacent sequences: A188212 A188213 A188214 * A188216 A188217 A188218 KEYWORD nonn,base AUTHOR Grant Garcia, Mar 24 2011 EXTENSIONS Program added by Grant Garcia, Mar 30 2011 Edited by Grant Garcia, Apr 13 2011 STATUS approved

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Last modified October 2 05:37 EDT 2023. Contains 365831 sequences. (Running on oeis4.)