A365017 a(n) is the least nonnegative integer not already in the sequence whose binary expansion is not the concatenation of any two earlier terms.

0, 1, 3, 4, 5, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 38, 39, 46, 47, 60, 61, 64, 65, 66, 68, 69, 70, 72, 73, 74, 80, 81, 82, 84, 85, 86, 88, 89, 90, 96, 97, 98, 100, 101, 104, 105, 106, 108, 109, 115, 119, 126, 127, 134, 135, 142, 143, 151, 156, 157, 158, 166, 167, 174

Offset

1,3

Comments

a(1)=0 is taken to be a single 0 bit when concatenating.

Links

Table of n, a(n) for n=1..66.

Attila Kiss, Java code to generate terms.

Example

The number 2 is excluded because its binary expansion is "10", which is the concatenation of a(1)="1" and a(0)="0".
The number 19 is excluded because its binary expansion is "10011", which is the concatenation of a(4)="100" and a(3)="11".

Mathematica

conc[x_, y_] := FromDigits[Flatten@IntegerDigits[{x, y}, 2], 2]; a[1] = 0; a[n_] := a[n] = Module[{k = a[n - 1] + 1, v = Array[a, n - 1], c}, c = conc @@@ Select[Tuples[v, {2}], UnsameQ @@ # &]; While[! FreeQ[c, k], k++]; k]; Array[a, 60] (* Amiram Eldar, Sep 29 2023 *)

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, bins, concats = 0, {"0"}, set()
    while True:
        yield an
        while (bn:=bin(an:=an+1)[2:]) in concats: pass
        concats |= {bn+bi for bi in bins} | {bi+bn for bi in bins}
        bins.add(bn)
print(list(islice(agen(), 62))) # Michael S. Branicky, Sep 29 2023

Crossrefs

Cf. A365018, A364871.

Sequence in context: A352908 A211518 A049895 * A226117 A221173 A346599

Adjacent sequences: A365014 A365015 A365016 * A365018 A365019 A365020

Keyword

nonn,base

Author

Attila Kiss, Aug 16 2023

Status

approved