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A333531
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 m.
3
3, 6, 10, 6, 8, 15, 8, 11, 21, 28, 13, 36, 10, 11, 16, 23, 45, 13, 28, 55, 18, 23, 66, 21, 27, 78, 16, 46, 91, 15, 18, 20, 23, 36, 53, 105, 26, 41, 120, 136, 21, 28, 52, 77, 153, 23, 31, 58, 86, 171, 40, 49, 190, 21, 23, 33, 44, 54, 71, 210, 23, 26, 36, 41, 78, 116, 231, 28, 253
OFFSET
1,1
LINKS
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], 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:=(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:
CROSSREFS
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: A337771 A232175 A065234 * A082184 A080817 A139762
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 01 2020
STATUS
approved