A368398 Iterates of the Christmas tree pattern map (A367508), where each row is interpreted as a single binary word and converted to decimal.

1, 2, 7, 37, 22, 95, 10, 2203, 12, 1117, 622, 4991, 661, 598, 542327, 793, 346, 271739, 412, 136637, 72158, 1154559, 42, 166507, 44, 149869, 141742, 545667567, 50, 199795, 52, 83317, 75190, 272971255, 56, 99961, 42682, 136623867, 51004, 68474749, 35186622, 1125971967

Offset

1,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..13494 (first 15 orders).

Example

The first 4 tree pattern orders of A367508 are shown below (left). In the middle the elements of each row are joined into single words; decimal conversion is on the right.
.
Order 1:                        |                        |
              0  1              |           01           |     1
                                |                        |
Order 2:                        |                        |
               10               |           10           |     2
           00  01  11           |         000111         |     7
                                |                        |
Order 3:                        |                        |
            100  101            |         100101         |    37
            010  110            |         010110         |    22
       000  001  011  111       |      000001011111      |    95
                                |                        |
Order 4:                        |                        |
              1010              |          1010          |    10
        1000  1001  1011        |      100010011011      |  2203
              1100              |          1100          |    12
        0100  0101  1101        |      010001011101      |  1117
        0010  0110  1110        |      001001101110      |   622
  0000  0001  0011  0111  1111  |  00000001001101111111  |  4991
.

Mathematica

With[{imax=7}, Map[FromDigits[StringJoin[#], 2]&, NestList[Map[Delete[{If[Length[#]>1, Map[#<>"0"&, Rest[#]], Nothing], Join[{#[[1]]<>"0"}, Map[#<>"1"&, #]]}, 0]&], {{"0", "1"}}, imax-1], {2}]] (* Generates terms up to order 7 *)

Prog

(Python)
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 int("".join(r), 2)
        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(), 42))) # Michael S. Branicky, Dec 26 2023

Crossrefs

Cf. A367508, A367555, A367562.

Sequence in context: A203900 A209251 A366670 * A274904 A173827 A029990

Adjacent sequences: A368395 A368396 A368397 * A368399 A368400 A368401

Keyword

nonn,base

Author

Paolo Xausa, Dec 22 2023

Status

approved