|
|
A130889
|
|
a(n) = smallest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.
|
|
6
|
|
|
0, 0, 5, 5, 11, 9, 17, 19, 29, 29, 31, 37, 47, 13, 59, 5, 5, 71, 71, 71, 9, 29, 31, 9, 107, 103, 5, 5, 131, 43, 131, 11, 5, 157, 167, 51, 5, 191, 7, 197, 199, 29, 5, 43, 227, 233, 233, 223, 257, 15, 9, 263, 281, 281, 281, 97, 13, 59, 317, 7, 17, 17, 47, 11, 353, 71, 349, 379, 389
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
a(n) is the "weight" of lucky numbers.
The decomposition of lucky numbers into weight * level + gap is A000959(n) = a(n) * A184828(n) + A031883(n) if a(n) > 0.
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 1 we have A000959(n) = 1, A000959(n+1) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0.
For n = 3 we have A000959(n) = 7, A000959(n+1) = 9; 5 is the smallest k such that 9 - 7 = 2 = (7 mod k), hence a(3) = 5.
For n = 24 we have A000959(n) = 105, A000959(n+1) = 111; 9 is the smallest k such that 111 - 105 = 6 = (105 mod k), hence a(24) = 9.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|