Superincreasing sequence
In mathematics, a sequence of positive real numbers is called superincreasing if every element of the sequence is greater than the sum of all previous elements in the sequence. [1][2]
Formally, written:
Example
For example, (1,3,6,13,27,52) is a superincreasing sequence, but (1,3,4,9,15,25) is not.[2] The following Python source code tests a sequence of numbers to determine if it is superincreasing:
sequence = [1, 3, 6, 13, 27, 52]
total = 0
test = True
for n in sequence:
print("Sum: ", total, "Element: ", n)
if n <= total:
test = False
break
total += n
print("Superincreasing sequence? ", test)
This produces the following output:
Sum: 0 Element: 1 Sum: 1 Element: 3 Sum: 4 Element: 6 Sum: 10 Element: 13 Sum: 23 Element: 27 Sum: 50 Element: 52 Superincreasing sequence? True
gollark: Assuming that that allows me to do one chunk per 15 seconds (linear speedup), it'd only take 130 days of turtle runtime.
gollark: If I spent a lot of krist on lasers I could plausibly get 128 or so, enough to cover half a chunk at once.
gollark: It'd take a year at optimal speeds. Probably more in practice since a player would need to be there to manage them.
gollark: 32 GTech™ experimental laser drills could plausibly clear a chunk in a minute or so. There are (14000/16)² chunks. Oh no.
gollark: Self replicating turtles and/or lasers.
See also
- Merkle-Hellman knapsack cryptosystem
References
- Richard A. Mollin, An Introduction to Cryptography (Discrete Mathematical & Applications), Chapman & Hall/CRC; 1 edition (August 10, 2000), ISBN 1-58488-127-5
- Bruce Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, pages 463-464, Wiley; 2nd edition (October 18, 1996), ISBN 0-471-11709-9
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.