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A247765
Table of denominators in the Egyptian fraction representation of n/(n+1) by the greedy algorithm.
3
2, 2, 6, 2, 4, 2, 4, 20, 2, 3, 2, 3, 42, 2, 3, 24, 2, 3, 18, 2, 3, 15, 2, 3, 14, 231, 2, 3, 12, 2, 3, 12, 156, 2, 3, 11, 231, 2, 3, 10, 2, 3, 10, 240, 2, 3, 10, 128, 32640, 2, 3, 9, 2, 3, 9, 342, 2, 3, 9, 180, 2, 3, 9, 126, 2, 3, 9, 99, 2, 3, 9, 83, 34362
OFFSET
1,1
COMMENTS
A100678(n) = length of n-th row;
T(n, A100678(n)) = A100695(n).
LINKS
Seiichi Manyama, Rows n = 1..1000 of triangle, flattened (Rows n = 1..100 from Reinhard Zumkeller)
EXAMPLE
. 1: 2
. 2: 2, 6
. 3: 2, 4
. 4: 2, 4, 20
. 5: 2, 3
. 6: 2, 3, 42
. 7: 2, 3, 24
. 8: 2, 3, 18
. 9: 2, 3, 15
. 10: 2, 3, 14, 231
. 11: 2, 3, 12
. 12: 2, 3, 12, 156
. 13: 2, 3, 11, 231
. 14: 2, 3, 10
. 15: 2, 3, 10, 240
. 16: 2, 3, 10, 128, 32640
. 17: 2, 3, 9
. 18: 2, 3, 9, 342
. 19: 2, 3, 9, 180
. 20: 2, 3, 9, 126
PROG
(Haskell)
import Data.Ratio ((%), numerator, denominator)
a247765 n k = a247765_tabf !! (n-1) !! (k-1)
a247765_tabf = map a247765_row [1..]
a247765_row n = f (map recip [2..]) (n % (n + 1)) where
f es x | numerator x == 1 = [denominator x]
| otherwise = g es
where g (u:us) | u <= x = (denominator u) : f us (x - u)
| otherwise = g us
CROSSREFS
Sequence in context: A110141 A339489 A293443 * A129750 A278234 A349330
KEYWORD
nonn,tabf
AUTHOR
Reinhard Zumkeller, Sep 25 2014
STATUS
approved