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A350605
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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 set {k, 2*k+1, 3*k+1: k in S_n}.
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2
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1, 1, 3, 4, 1, 3, 4, 7, 9, 10, 13, 1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 40, 1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 64, 67, 81, 82, 85, 94, 121, 1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 64, 67, 79, 81, 82, 85, 87, 91, 93, 94, 111, 115, 117, 118, 121, 127, 129, 130, 135, 136, 139, 163, 165, 166, 171, 172, 175, 189, 190, 193, 202, 243, 244, 247, 256, 283, 364
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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The first few sets S_n are:
[1],
[1, 3, 4],
[1, 3, 4, 7, 9, 10, 13],
[1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 40],
[1, 3, 4, 7, 9, 10, 13, 15, 19, 21, 22, 27, 28, 31, 39, 40, 43, 45, 46, 55, 57, 58, 63, 64, 67, 81, 82, 85, 94, 121],
...
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MAPLE
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T:= proc(n) option remember; `if`(n=1, 1, sort(
[map(k-> [k, 2*k+1, 3*k+1][], {T(n-1)})[]])[])
end:
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MATHEMATICA
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T[n_] := T[n] = If[n==1, {1}, {#, 2#+1, 3#+1}& /@ T[n-1] // Flatten //
Union];
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PROG
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(Python)
from itertools import chain, islice
def A350605_gen(): # generator of terms
s = {1}
while True:
yield from sorted(s)
s = set(chain.from_iterable((x, 2*x+1, 3*x+1) 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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