A198456
Consider triples a<=b
Original entry on oeis.org
3, 6, 10, 8, 15, 11, 21, 28, 13, 36, 16, 23, 45, 28, 55, 18, 23, 66, 21, 27, 78, 46, 91, 20, 23, 36, 53, 105, 26, 41, 120, 136, 28, 52, 77, 153, 31, 58, 86, 171, 40, 49, 190, 33, 44, 54, 71, 210, 36, 41, 78, 116
Offset: 1
2*3 + 2*3 = 3*4
3*4 + 5*6 = 6*7
4*5 + 9*10 = 10*11
5*6 + 6*7 = 8*9
5*6 + 14*15 = 15*16
6*7 + 9*10 = 11*12
- A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
A198455
Consider triples a<=b
Original entry on oeis.org
2, 5, 9, 6, 14, 9, 20, 27, 10, 35, 13, 21, 44, 26, 54, 14, 20, 65, 17, 24, 77, 44, 90, 14, 18, 33, 51, 104, 21, 38, 119, 135, 22, 49, 75, 152, 25, 55, 84, 170, 35, 45, 189, 26, 39, 50, 68, 209, 29, 35, 75, 114, 230, 125
Offset: 1
2*3 + 2*3 = 3*4
3*4 + 5*6 = 6*7
4*5 + 9*10 = 10*11
5*6 + 6*7 = 8*9
5*6 + 14*15 = 15*16
6*7 + 9*10 = 11*12
- A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
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.
Original entry on oeis.org
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
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
...
If we only take triples [n,k,m] with n <= k <= m, the values of k and m are
A198455 and
A198456 respectively.
-
# 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:
Showing 1-3 of 3 results.
Comments