A260618 - OEIS

%I #35 Nov 15 2024 01:43:58

%S 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,

%T 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,

%U 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

%N Irregular triangle read by rows: denominators of the expansion of k/n using the greedy algorithm, 1<=k<=n.

%H Seiichi Manyama, <a href="/A260618/b260618.txt">Rows n=1..81 of triangle, flattened</a> (Rows 1..29 from Andrew Howroyd)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions">Greedy algorithm for Egyptian fractions</a>

%e Triangle begins ({} included for fraction separation):

%e   {1};

%e   {2}, {1};

%e   {3}, {2, 6}, {1};

%e   {4}, {2}, {2, 4}, {1};

%e   {5}, {3, 15}, {2, 10}, {2, 4, 20}, {1};

%e   {6}, {3}, {2}, {2, 6}, {2, 3}, {1};

%e   {7}, {4, 28}, {3, 11, 231}, {2, 14}, {2, 5, 70}, {2, 3, 42}, {1};

%e   {8}, {4}, {3, 24}, {2}, {2, 8}, {2, 4}, {2, 3, 24}, {1};

%e   {9}, {5, 45}, {3}, {3, 9}, {2, 18}, {2, 6}, {2, 4, 36}, {2, 3, 18}, {1};

%e   {10}, {5}, {4, 20}, {3, 15}, {2}, {2, 10}, {2, 5}, {2, 4, 20}, {2, 3, 15}, {1};

%e   {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};

%o (PARI)

%o rep(f)={L=List(); while(f<>0, my(t=ceil(1/f)); listput(L,t); f-=1/t); Vec(L)}

%o row(n)={concat(apply(k->rep(k/n), [1..n]))}

%o for(n=1, 11, print(row(n))) \\ _Andrew Howroyd_, Feb 26 2018

%Y Cf. A050205, A050206, A050210, A098853, A100140.

%K nonn,tabf

%O 1,2

%A _Matthew Campbell_, Sep 17 2015