

A216993


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


3



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, 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, 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
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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. 340342


LINKS



EXAMPLE

Row 5 = [2,4,10,12,15]: lexicographically earliest denominators with the least possible maximum value (15) among 72 possible 5term 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



AUTHOR



STATUS

approved



