A136375 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.

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

Offset

0,2

Links

Table of n, a(n) for n=0..45.

Example

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).

Crossrefs

Cf. A000367, A002445.

Row sums: A151711. - N. J. A. Sloane, Jun 07 2009

Sequence in context: A062268 A067879 A334900 * A138706 A027762 A002445

Adjacent sequences: A136372 A136373 A136374 * A136376 A136377 A136378

Keyword

more,nonn,tabf

Author

Leroy Quet, Mar 29 2008

Extensions

Row 6 from N. J. A. Sloane, Jun 07 2009

Better definition and more terms from T. D. Noe, Jun 07 2009

Status

approved