|
Search: id:A111684
|
|
|
| A111684 |
|
Least k such that product of n successive numbers beginning with k exceeds n^n. |
|
+0
1
|
|
| 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 41, 41
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Least k such that Pochhammer(k, n) > n^n. - Ryan Propper (rpropper(AT)stanford.edu), Sep 06 2005
lim(n->infinity) a(n)/n converges to the value in sequence A090462: 0.542211419737745110564407530431280310406389370587047470415565901319480898043509307495187652042776923596... - Ryan Propper (rpropper(AT)stanford.edu), Sep 06 2005
|
|
LINKS
|
Eric Weisstein. "Pochhammer Symbol".
|
|
EXAMPLE
|
a(4) = 3, 2*3*4*5 = 120 < 256 =4^4 < 3*4*5*6 =360.
|
|
MATHEMATICA
|
Do[k = 1; While[Pochhammer[k, n] <= n^n, k++ ]; Print[k], {n, 1, 100}] (Propper)
|
|
CROSSREFS
|
Adjacent sequences: A111681 A111682 A111683 this_sequence A111685 A111686 A111687
Sequence in context: A096740 A026830 A025155 this_sequence A025159 A026829 A025154
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 16 2005
|
|
EXTENSIONS
|
More terms from Ryan Propper (rpropper(AT)stanford.edu), Sep 06 2005
|
|
|
Search completed in 0.002 seconds
|
