A367726 - OEIS

%I #18 Nov 30 2023 07:14:14

%S 1,2,4,9,8,11,10,28,12,22,22,26,41,40,75,49,36,55,40,51,52,57,42,124,

%T 44,118,118,186,50,148,52,94,94,130,56,106,94,114,100,112,114,120,169,

%U 168,331,177,164,311,168,307,308,441,201,200,395,209,148,231,152,227

%N Row sums of A367562 (iterates of the Christmas tree pattern map, A367508, converted to decimal).

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

%H Paolo Xausa, <a href="/A367726/b367726.txt">Table of n, a(n) for n = 1..13494</a> (first 15 orders).

%H Michael De Vlieger, <a href="/A367726/a367726.png">Log log scatterplot of a(n)</a>, n = 1..99294 (18 orders) showing primes in red, and nonprimes in dark green.

%H Michael De Vlieger, <a href="/A367726/a367726_1.png">Log log scatterplot of a(n)</a>, n = 1..7059 (14 orders) showing primes in red, composite prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue, accentuating numbers of the last category that are also squareful in light blue.

%e The first 4 tree pattern orders of A367508 are shown below (left). In the middle they are converted to decimal (A367562); row sums are on the right.

%e .

%e Order 1:                        |                 |

%e               0  1              |      0  1       |   1

%e                                 |                 |

%e Order 2:                        |                 |

%e                10               |        2        |   2

%e            00  01  11           |     0  1  3     |   4

%e                                 |                 |

%e Order 3:                        |                 |

%e             100  101            |      4  5       |   9

%e             010  110            |      2  6       |   8

%e        000  001  011  111       |   0  1  3  7    |  11

%e                                 |                 |

%e Order 4:                        |                 |

%e               1010              |       10        |  10

%e         1000  1001  1011        |     8  9 11     |  28

%e               1100              |       12        |  12

%e         0100  0101  1101        |     4  5 13     |  22

%e         0010  0110  1110        |     2  6 14     |  22

%e   0000  0001  0011  0111  1111  |  0  1  3  7 15  |  26

%e .

%t With[{imax=8},Map[Total,Map[FromDigits[#,2]&,NestList[Map[Delete[{If[Length[#]>1,Map[#<>"0"&,Rest[#]],Nothing],Join[{#[[1]]<>"0"},Map[#<>"1"&,#]]},0]&],{{"0","1"}},imax-1],{3}],{2}]] (* Generates terms up to order 8 *)

%o (Python)

%o from itertools import islice

%o from functools import reduce

%o def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])

%o def agen():  # generator of terms

%o     R = [["0", "1"]]

%o     while R:

%o         r = R.pop(0)

%o         yield sum(map(lambda b: int(b, 2), r))

%o         if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))

%o         R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))

%o print(list(islice(agen(), 60))) # _Michael S. Branicky_, Nov 28 2023

%Y Cf. A367508, A367562.

%K nonn,base,look

%O 1,2

%A _Paolo Xausa_, Nov 28 2023