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A350604
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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.
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3
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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
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OFFSET
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1,3
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COMMENTS
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S_n contains n*(n+1)/2 elements.
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LINKS
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EXAMPLE
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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],
...
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MAPLE
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T:= proc(n) option remember; `if`(n=1, 1, sort(
[map(k-> [k, 2*k, 3*k][], {T(n-1)})[]])[])
end:
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MATHEMATICA
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S[1] = {1};
S[n_] := S[n] = Union[S[n-1], 2*S[n-1], 3*S[n-1]];
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PROG
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(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))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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