A350604 Irregular triangle read by rows: row n lists the elements of the set S_n in increasing order, where S_1 = {1}, and S_{n+1} is the union of S_n, 2*S_n, and 3*S_n.
1, 1, 2, 3, 1, 2, 3, 4, 6, 9, 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 54, 81, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 108, 162, 243, 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 216, 243, 324, 486, 729
Offset: 1
Examples
The first few sets S_n are: [1], [1, 2, 3], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 8, 9, 12, 18, 27], [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 54, 81], [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 108, 162, 243], ...
Links
- Alois P. Heinz, Rows n = 1..50, flattened
Programs
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Maple
T:= proc(n) option remember; `if`(n=1, 1, sort( [map(k-> [k, 2*k, 3*k][], {T(n-1)})[]])[]) end: seq(T(n), n=1..7); # Alois P. Heinz, Jan 12 2022 -
Mathematica
S[1] = {1}; S[n_] := S[n] = Union[S[n-1], 2*S[n-1], 3*S[n-1]]; Table[S[n], {n, 1, 7}] // Flatten (* Jean-François Alcover, Jun 02 2022 *) -
Python
from itertools import chain, islice def A350604_gen(): # generator of terms s = {1} while True: yield from sorted(s) s = set(chain.from_iterable((x,2*x,3*x) for x in s)) A350604_list = list(islice(A350604_gen(),30)) # Chai Wah Wu, Jan 12 2022
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