A368431 -id:A368431 - cp's OEIS frontend

A368432 Inverse permutation to A368431.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 8, 11, 12, 13, 14, 15, 20, 21, 18, 22, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 43, 44, 40, 45, 37, 38, 41, 46, 33, 34, 32, 35, 36, 39, 42, 47, 49, 50, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 90, 91, 86, 92

Offset: 0

Rémy Sigrist, Dec 24 2023

			A368431(42) = 46, so a(46) = 42.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A368431.

PARI
```
See Links section.
```

from itertools import islice
from functools import reduce
def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
def A368431gen():  # generator of A368431
    R, aset = [["0", "1"]], set()
    while R:
        r = R.pop(0)
        for b in r:
            d = int(b, 2)
            if d not in aset: yield d; aset.add(d)
        if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
        R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
def agen(): # generator of terms
    adict, n = dict(), 0
    for i, k in enumerate(A368431gen()):
        if k not in adict:
            adict[k] = i
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Dec 24 2023

A367562 Iterates of the Christmas tree pattern map (A367508), read by rows and converted to decimal.

Original entry on oeis.org

0, 1, 2, 0, 1, 3, 4, 5, 2, 6, 0, 1, 3, 7, 10, 8, 9, 11, 12, 4, 5, 13, 2, 6, 14, 0, 1, 3, 7, 15, 20, 21, 18, 22, 16, 17, 19, 23, 24, 25, 10, 26, 8, 9, 11, 27, 12, 28, 4, 5, 13, 29, 2, 6, 14, 30, 0, 1, 3, 7, 15, 31, 42, 40, 41, 43, 44, 36, 37, 45, 34, 38, 46, 32, 33, 35, 39, 47

Offset: 1

Paolo Xausa, Nov 23 2023

See A367508 for the description of the Christmas tree patterns, references and links.

			The first 4 tree pattern orders are shown below (on the right their elements are converted to decimal: the present sequence is obtained by reading the right half of the diagram left to right, top to bottom).
The sequence of the terms in chains of length 1 (marked with asterisks) coincides with the positive terms of A014486.
.
Order 1:                        |
              0  1              |      0  1
                                |
Order 2:                        |
               10               |        2*
           00  01  11           |     0  1  3
                                |
Order 3:                        |
            100  101            |      4  5
            010  110            |      2  6
       000  001  011  111       |   0  1  3  7
                                |
Order 4:                        |
              1010              |       10*
        1000  1001  1011        |     8  9 11
              1100              |       12*
        0100  0101  1101        |     4  5 13
        0010  0110  1110        |     2  6 14
  0000  0001  0011  0111  1111  |  0  1  3  7 15
.

Paolo Xausa, Table of n, a(n) for n = 1..8190 (first 12 orders, flattened).

Cf. A014486, A367508, A367555, A367726, A367951, A367953, A368400, A368431.

With[{imax=6},Map[FromDigits[#,2]&,NestList[Map[Delete[{If[Length[#]>1,Map[#<>"0"&,Rest[#]],Nothing],Join[{#[[1]]<>"0"},Map[#<>"1"&,#]]},0]&],{{"0","1"}},imax-1],{3}]] (* Generates terms up to order 6 *)

from itertools import islice
from functools import reduce
def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
def agen():  # generator of terms
    R = [["0", "1"]]
    while R:
        r = R.pop(0)
        yield from map(lambda b: int(b, 2), r)
        if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
        R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
print(list(islice(agen(), 77))) # Michael S. Branicky, Nov 23 2023

cp's OEIS Frontend

A368432 Inverse permutation to A368431.

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