|
|
A299438
|
|
a(n) is the smallest number k such that there do not exist k numbers in the range [1..n] whose product is equal to their sum or -1 if no such number exists.
|
|
2
|
|
|
2, 3, 4, 6, 6, 15, 15, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 80, 80, 80, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114, 114
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If a(n) > 0 for all n, then sequence is nondecreasing and a(n) > n.
For n >= 38, a(n) appears to follow the pattern: a(n) = k_m for k_{m-1} <= n < k_m, for a sequence of numbers {k_m} = {38, 114, 174, 444, 4354, ... }.
Conjecture: a(n) > 0 for all n.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) > 1 since the product of the list (1) is the same as its product. a(1) = 2 since the product of the list (1,1) = 1 which is not the same as its sum (= 2).
a(2) > 2 since (2,2) has both product and sum equal to 2. Similarly a(3) > 3 since (1,2,3) has both sum and product equal to 6.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|