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A216993 Triangle read by rows in which row n gives the lexicographically earliest denominators with the least possible maximum value among all n-term Egyptian fractions with unit sum.

%I A216993 #40 Feb 16 2025 08:33:18
%S A216993 1,0,0,2,3,6,2,4,6,12,2,4,10,12,15,3,4,6,10,12,15,3,4,9,10,12,15,18,3,
%T A216993 5,9,10,12,15,18,20,4,5,8,9,10,15,18,20,24,5,6,8,9,10,12,15,18,20,24,
%U A216993 5,6,8,9,10,15,18,20,21,24,28,4,8,9,10,12,15,18,20,21,24,28,30,4,8,9,11,12,18,20,21,22,24,28,30,33
%N A216993 Triangle read by rows in which row n gives the lexicographically earliest denominators with the least possible maximum value among all n-term Egyptian fractions with unit sum.
%C A216993 This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimum largest denominator given in A030659.
%C A216993 Row 2 = [0,0] corresponds to the fact that 1 cannot be written as an Egyptian fraction with 2 (distinct) terms.
%H A216993 Robert Price, <a href="/A216993/b216993.txt">Rows n = 1..24, flattened</a>
%H A216993 Mohammad K. Azarian, <a href="http://www.jstor.org/stable/10.4169/college.math.j.42.4.329">Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958</a>, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330.
%H A216993 Mohammad K. Azarian, <a href="http://www.jstor.org/stable/10.4169/college.math.j.43.4.337">Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Solution</a> College Mathematics Journal, Vol. 43, No. 4, September 2012, pp. 340-342.
%H A216993 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 A216993 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A216993 Wikipedia, <a href="http://en.wikipedia.org/wiki/Egyptian_fraction">Egyptian fraction</a>
%H A216993 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A216993 Row 5 = [2,4,10,12,15]: lexicographically earliest denominators with the least possible maximum value (15) among 72 possible 5-term Egyptian fractions equal to 1. 1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15.
%e A216993 Triangle begins:
%e A216993   1;
%e A216993   0, 0;
%e A216993   2, 3,  6;
%e A216993   2, 4,  6, 12;
%e A216993   2, 4, 10, 12, 15;
%e A216993   3, 4,  6, 10, 12, 15;
%Y A216993 Cf. A030659, A073546, A213062, A216975, A378723.
%K A216993 nonn,tabl
%O A216993 1,4
%A A216993 _Robert Price_, Sep 21 2012