A050206 - OEIS

%I #31 Sep 18 2022 14:31:39

%S 2,3,2,4,2,2,5,3,2,2,6,3,2,2,2,7,4,3,2,2,2,8,4,3,2,2,2,2,9,5,3,3,2,2,

%T 2,2,10,5,4,3,2,2,2,2,2,11,6,4,3,3,2,2,2,2,2,12,6,4,3,3,2,2,2,2,2,2,

%U 13,7,5,4,3,3,2,2,2,2,2,2,14,7,5,4,3,3,2,2,2,2,2,2,2,15,8,5,4,3,3,3,2

%N Triangle read by rows: smallest denominator of the expansion of k/n using the greedy algorithm, 1<=k<=n-1.

%H Seiichi Manyama, <a href="/A050206/b050206.txt">Rows n = 2..141, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitFraction.html">Unit Fraction</a>.

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

%F T(n,k) = ceiling(n/k).

%e n\k | 1  2  3  4  5  6  7  8

%e ----*------------------------

%e   2 | 2;

%e   3 | 3, 2;

%e   4 | 4, 2, 2;

%e   5 | 5, 3, 2, 2;

%e   6 | 6, 3, 2, 2, 2;

%e   7 | 7, 4, 3, 2, 2, 2;

%e   8 | 8, 4, 3, 2, 2, 2, 2;

%e   9 | 9, 5, 3, 3, 2, 2, 2, 2;

%Y Cf. A050205, A050210 (Largest denominator), A260618.

%K nonn,easy,tabl

%O 2,1

%A _Eric W. Weisstein_

%E Offset changed to 2 by _Seiichi Manyama_, Sep 18 2022