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A216975 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.

%I A216975 #34 Feb 16 2025 08:33:18
%S A216975 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 A216975 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 A216975 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 A216975 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 A216975 This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimal sum given in A213062.
%C A216975 Row 2 = [0,0] corresponds to the fact that 1 cannot be written as Egyptian fraction with 2 (distinct) terms.
%D A216975 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 A216975 Robert Price, <a href="/A216975/b216975.txt">Rows n = 1..24, flattened</a>
%H A216975 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 A216975 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A216975 Wikipedia, <a href="http://en.wikipedia.org/wiki/Egyptian_fraction">Egyptian fraction</a>
%H A216975 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A216975 Row 5 = [3,4,5,6,20]: lexicographically earliest minimal sum (38) denominators among 72 possible 5-term Egyptian fractions with unit sum.
%e A216975 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20.
%e A216975 Triangle begins:
%e A216975 1;
%e A216975 0, 0;
%e A216975 2, 3, 6;
%e A216975 2, 4, 6, 12;
%e A216975 3, 4, 5,  6, 20;
%e A216975 3, 4, 6, 10, 12, 15;
%Y A216975 Cf. A030659, A073546, A213062, A216993.
%K A216975 nonn,tabl
%O A216975 1,4
%A A216975 _Robert Price_, Sep 21 2012