A050210
Largest denominator in unit fraction representation of triangle of numbers 1/2, 1/3, 2/3, 1/4, 2/4, ... as computed with greedy algorithm.
Original entry on oeis.org
2, 3, 6, 4, 2, 4, 5, 15, 10, 20, 6, 3, 2, 6, 3, 7, 28, 231, 14, 70, 42, 8, 4, 24, 2, 8, 4, 24, 9, 45, 3, 9, 18, 6, 36, 18, 10, 5, 20, 15, 2, 10, 5, 20, 15, 11, 66, 44, 33, 99, 22, 88, 4070, 660, 231, 12, 6, 4, 3, 12, 2, 12, 6, 4, 3, 12, 13, 91, 2145, 468, 780, 312, 26, 234, 39, 52, 78, 156
Offset: 2
Triangle begins:
2;
3, 6;
4, 2, 4;
5, 15, 10, 20;
6, 3, 2, 6, 3;
7, 28, 231, 14, 70, 42;
8, 4, 24, 2, 8, 4, 24;
9, 45, 3, 9, 18, 6, 36, 18;
10, 5, 20, 15, 2, 10, 5, 20, 15;
11, 66, 44, 33, 99, 22, 88, 4070, 660, 231;
...
A050205
Triangle read by rows: number of terms in unit fraction representation of k/n using the greedy algorithm, 1<=k<=n-1.
Original entry on oeis.org
1, 1, 2, 1, 1, 2, 1, 2, 2, 3, 1, 1, 1, 2, 2, 1, 2, 3, 2, 3, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 3, 3, 1, 1, 2, 2, 1, 2, 2, 3, 3, 1, 2, 2, 2, 3, 2, 3, 4, 4, 4, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 3, 3, 4, 1, 2, 1, 2, 1, 2, 3, 2, 2, 2, 3
Offset: 2
2/3 = 1/2 + 1/6. So T(3,2) = 2.
n\k | 1 2 3 4 5 6 7 8
----*------------------------
2 | 1;
3 | 1, 2;
4 | 1, 1, 2;
5 | 1, 2, 2, 3;
6 | 1, 1, 1, 2, 2;
7 | 1, 2, 3, 2, 3, 3;
8 | 1, 1, 2, 1, 2, 2, 3;
9 | 1, 2, 1, 2, 2, 2, 3, 3;
A260618
Irregular triangle read by rows: denominators of the expansion of k/n using the greedy algorithm, 1<=k<=n.
Original entry on oeis.org
1, 2, 1, 3, 2, 6, 1, 4, 2, 2, 4, 1, 5, 3, 15, 2, 10, 2, 4, 20, 1, 6, 3, 2, 2, 6, 2, 3, 1, 7, 4, 28, 3, 11, 231, 2, 14, 2, 5, 70, 2, 3, 42, 1, 8, 4, 3, 24, 2, 2, 8, 2, 4, 2, 3, 24, 1, 9, 5, 45, 3, 3, 9, 2, 18, 2, 6, 2, 4, 36, 2, 3, 18, 1, 10, 5, 4, 20, 3, 15, 2, 2, 10, 2, 5, 2, 4, 20, 2, 3, 15, 1, 11, 6, 66, 4, 44, 3, 33, 3, 9, 99, 2, 22, 2, 8, 88, 2, 5, 37, 4070, 2, 4, 15, 660, 2, 3, 14, 231, 1
Offset: 1
Triangle begins ({} included for fraction separation):
{1};
{2}, {1};
{3}, {2, 6}, {1};
{4}, {2}, {2, 4}, {1};
{5}, {3, 15}, {2, 10}, {2, 4, 20}, {1};
{6}, {3}, {2}, {2, 6}, {2, 3}, {1};
{7}, {4, 28}, {3, 11, 231}, {2, 14}, {2, 5, 70}, {2, 3, 42}, {1};
{8}, {4}, {3, 24}, {2}, {2, 8}, {2, 4}, {2, 3, 24}, {1};
{9}, {5, 45}, {3}, {3, 9}, {2, 18}, {2, 6}, {2, 4, 36}, {2, 3, 18}, {1};
{10}, {5}, {4, 20}, {3, 15}, {2}, {2, 10}, {2, 5}, {2, 4, 20}, {2, 3, 15}, {1};
{11}, {6, 66}, {4, 44}, {3, 33}, {3, 9, 99}, {2, 22}, {2, 8, 88}, {2, 5, 37, 4070}, {2, 4, 15, 660}, {2, 3, 14, 231}, {1};
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rep(f)={L=List(); while(f<>0, my(t=ceil(1/f)); listput(L,t); f-=1/t); Vec(L)}
row(n)={concat(apply(k->rep(k/n), [1..n]))}
for(n=1, 11, print(row(n))) \\ Andrew Howroyd, Feb 26 2018
Showing 1-3 of 3 results.