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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. 5
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimal sum given in A213062. Row 2 = [0,0] corresponds to the fact that 1 cannot be written as Egyptian fraction with 2 (distinct) terms. REFERENCES 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 LINKS Robert Price, Rows n = 1..24, flattened Harry Ruderman and Paul Erdős, Problem E2427: Bounds for Egyptian fraction partitions of unity (comments), Amer. Math. Monthly, 1974 (Vol. 81), pp. 780-782. Eric Weisstein's World of Mathematics, Egyptian Fraction Wikipedia, Egyptian fraction EXAMPLE Row 5 = [3,4,5,6,20]: lexicographically earliest minimal sum (38) denominators among 72 possible 5-term Egyptian fractions with unit sum. 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20. Triangle begins: 1; 0, 0; 2, 3, 6; 2, 4, 6, 12; 3, 4, 5, 6, 20; 3, 4, 6, 10, 12, 15; CROSSREFS Cf. A030659, A073546, A213062, A216993. Sequence in context: A275734 A216993 A073546 * A275666 A330666 A319432 Adjacent sequences: A216972 A216973 A216974 * A216976 A216977 A216978 KEYWORD nonn,tabl AUTHOR Robert Price, Sep 21 2012 STATUS approved

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Last modified December 7 05:41 EST 2022. Contains 358649 sequences. (Running on oeis4.)