OFFSET
1,3
COMMENTS
S_n contains n*(n+1)/2 elements.
The rows converge to A003586.
LINKS
Alois P. Heinz, Rows n = 1..50, flattened
EXAMPLE
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],
...
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 *)
PROG
(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))
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Jan 12 2022
STATUS
approved