

A333530


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.


3



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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..69.
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000, April 2020


EXAMPLE

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
...


MAPLE

# 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:=(mami1)/2;
m:=(ma+mi1)/2;
# skip if k=0
if k>0 then
lprint(n, k, m);
fi;
fi;
od:
od:


CROSSREFS

Cf. A000217, A309507, A333529, A333531.
If we only take triples [n,k,m] with n <= k <= m, the values of k and m are A198455 and A198456 respectively.
Sequence in context: A324835 A082183 A332554 * A111474 A111761 A021798
Adjacent sequences: A333527 A333528 A333529 * A333531 A333532 A333533


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 01 2020


STATUS

approved



