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.

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

Offset: 1

Author

N. J. A. Sloane, Apr 01 2020

Keywords

• nonn

Examples

			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
...
		

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.

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.

Programs

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: