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

Author

Paolo Xausa, Dec 22 2023

Keywords

• nonn
• base

Comments

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

Examples

			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
.
		

Links

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

Crossrefs

Cf. A367508, A367555, A367562.

Programs

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 *)

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