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A136375
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Irregular array read by rows, where n-th row gives denominators of the Egyptian fraction expansion, derived using the greedy algorithm, for the absolute value of the fractional part of the (2n)th Bernoulli number.
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1
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0, 6, 30, 42, 30, 14, 231, 4, 322, 125580, 6, 11, 802, 1124805, 2, 3, 8, 78, 41496, 9, 77, 6930, 9, 83, 34362, 4, 322, 125580, 6, 15, 870, 2, 3, 15, 1557, 9291398, 172660144297410, 11, 802, 1124805, 6, 4, 13, 171, 885780, 6
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OFFSET
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0,2
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LINKS
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EXAMPLE
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Triangle begins:
0,
6,
30,
42,
30,
14, 231
4, 322, 125580
...
The 10th Bernoulli number is 5/66. The largest unit fraction <= 5/66 is 1/14. Now 5/66 - 1/14 is 1/231, which is itself a unit fraction. So the Egyptian fraction representation of 5/66 is 1/14 + 1/231. Therefore row 5 of this array is (14,231).
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CROSSREFS
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KEYWORD
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more,nonn,tabf
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AUTHOR
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EXTENSIONS
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Better definition and more terms from T. D. Noe, Jun 07 2009
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STATUS
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approved
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