%I #33 Jul 21 2015 11:31:50

%S 1,0,0,2,3,6,2,4,6,12,3,4,5,6,20,3,4,6,10,12,15,3,4,9,10,12,15,18,4,5,

%T 6,9,10,15,18,20,4,6,8,9,10,12,15,18,24,5,6,8,9,10,12,15,18,20,24,6,7,

%U 8,9,10,12,14,15,18,24,28,6,7,9,10,11,12,14,15,18,22,28,33,7,8,9,10,11,12,14,15,18,22,24,28,33

%N Triangle read by rows in which row n gives the lexicographically earliest minimal sum denominators among all possible n-term Egyptian fractions with unit sum.

%C This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimal sum given in A213062.

%C Row 2 = [0,0] corresponds to the fact that 1 cannot be written as Egyptian fraction with 2 (distinct) terms.

%D Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

%H Robert Price, <a href="/A216975/b216975.txt">Rows n = 1..24, flattened</a>

%H Harry Ruderman and Paul Erdős, <a href="http://www.jstor.org/stable/2319578">Problem E2427: Bounds for Egyptian fraction partitions of unity</a> (comments), Amer. Math. Monthly, 1974 (Vol. 81), pp. 780-782.

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Egyptian_fraction">Egyptian fraction</a>

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%e Row 5 = [3,4,5,6,20]: lexicographically earliest minimal sum (38) denominators among 72 possible 5-term Egyptian fractions with unit sum.

%e 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20.

%e Triangle begins:

%e 1;

%e 0, 0;

%e 2, 3, 6;

%e 2, 4, 6, 12;

%e 3, 4, 5, 6, 20;

%e 3, 4, 6, 10, 12, 15;

%Y Cf. A030659, A073546, A213062, A216993.

%K nonn,tabl

%O 1,4

%A _Robert Price_, Sep 21 2012