Number Problems
1.0 Just a few easy sequences...
Find the next 3 terms of these sequences:
... 21, 34, 55, 89, 144 ...
3, 3, 5, 4, 4, 3 ...
2, 5, 14, 10 ...
2.0 Argh... more sequences!
2.1 Triangular Numbers
Triangular Numbers are numbers made by summing counting numbers. So the first
is 1, then 3 (1 + 2), then 6 (1 + 2 + 3) etc. What is the 100th?
Bonus points for working out how many Triangular Prime Numbers there are (below 1 000 000).
2.2 Prime Numbers
In a similar manner, find the first prime number after 1000.
2.3 Lonely Primes
There exists a set of numbers called "Lonely Numbers". A number X is not lonely
if there is another number Z whose digits summed, plus itself, are equal to
X.
So 15 is not-lonely as (12 + 1 + 2 = 15).
How many lonely primes below 50?
3.0 Did anyone happen to bring any?
Poe, E.
Near a Raven
Midnights so dreary, tired and weary.
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore".
4.0 Not more crypto!
yltktlcteiair
Bonus points if you can encrypt a message back to me in the same manner.