OFFSET
1,4
COMMENTS
This sequence is the lexicographically earliest Egyptian fraction (denominators only) describing the minimum largest denominator given in A030659.
Row 2 = [0,0] corresponds to the fact that 1 cannot be written as an 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 = [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.
Triangle begins:
1;
0, 0;
2, 3, 6;
2, 4, 6, 12;
2, 4, 10, 12, 15;
3, 4, 6, 10, 12, 15;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Robert Price, Sep 21 2012
STATUS
approved