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, 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

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

Chai Wah Wu, Table of n, a(n) for n = 1..450

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

Cf. A299439.

Sequence in context: A002729 A135510 A265398 * A030209 A265399 A138588

Adjacent sequences: A299435 A299436 A299437 * A299439 A299440 A299441

Keyword

nonn

Author

Chai Wah Wu, Feb 19 2018

Status

approved