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A333530
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Make a list of triples [n,k,m] with n>=1, k>=1, and T_n+T_k = T_m as in A309507, arranged in lexicographic order; sequence gives values of k.
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3
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2, 5, 9, 3, 6, 14, 5, 9, 20, 27, 10, 35, 4, 6, 13, 21, 44, 8, 26, 54, 14, 20, 65, 17, 24, 77, 9, 44, 90, 5, 11, 14, 18, 33, 51, 104, 21, 38, 119, 135, 12, 22, 49, 75, 152, 14, 25, 55, 84, 170, 35, 45, 189, 6, 11, 26, 39, 50, 68, 209, 9, 15, 29, 35, 75, 114, 230, 17, 252
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The first few triples are:
2, 2, 3
3, 5, 6
4, 9, 10
5, 3, 6
5, 6, 8
5, 14, 15
6, 5, 8
6, 9, 11
6, 20, 21
7, 27, 28
8, 10, 13
8, 35, 36
9, 4, 10
9, 6, 11
9, 13, 16
9, 21, 23
9, 44, 45
10, 8, 13
10, 26, 28
10, 54, 55
11, 14, 18
11, 20, 23
11, 65, 66
12, 17, 21
12, 24, 27
12, 77, 78
...
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MAPLE
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# This program produces the triples for each value of n, but then they need to be sorted on k:
with(numtheory):
A:=[]; M:=100;
for n from 1 to M do
TT:=n*(n+1);
dlis:=divisors(TT);
for d in dlis do
if (d mod 2) = 1 then e := TT/d;
mi:=min(d, e); ma:=max(d, e);
k:=(ma-mi-1)/2;
m:=(ma+mi-1)/2;
# skip if k=0
if k>0 then
lprint(n, k, m);
fi;
fi;
od:
od:
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CROSSREFS
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If we only take triples [n,k,m] with n <= k <= m, the values of k and m are A198455 and A198456 respectively.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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