here's a braincracker for you: 1,2,4,8,15,30,50,100...what's the next number? why?

Question

I bumpt into this sequence some time ago but as much as I've tryed I haven't found an answer as well as everybody else I know. Can you solve it? Please give the next answer to the sequence and explain your hypothesis.

PD: I don't think doubling will work if you haven't already noticed...

THANK YOU SO MUCH TO ANYONE WHO CAN PROVIDE ME WITH AN ACCURATE ANSWER

Answer 1

The squence is doubling every other number
consider every other number 1, 4, 15, 50

1 = start
- the next number X 2 = 2
4 = the previous 2 numbers + 1 (2 + 1 + 1 = 4)
- the next number X 2 = 8
15 = the previous 2 numbers + 3 = (8 + 4 + 3 = 15)
- the next number X 2 = 30
50 = the previous 2 numbers + 5 = (30 + 15 + 5 = 50)
- the next number X 2 = 100

Therefore, the sequence is 100 + 50 + 7 = 157

Answer 2

EDIT AGAIN - actually vijay it is still right. Choose any number such that the prime factors add to 16 it would satisfy it. However it is trivial knowledge to point out that there are infinite answers. The idea is to come up with SOME. Not to parade implied knowledge.

EDIT - I stand corrected. 14 = 7 + 7; 7^2 = 49 < 100. So the smallest factor idea isnt correct... but the general method still could be right. Although i like the answer above. Ultimately there is an infinite class of functions that satisfy this
END

Heres a thought

1 = 1x1; sum of prime factors 0 (1 is not prime)
2 = 2; 2
4 = 2 * 2; 4
8 = 2 * 2 * 2; 6
15 = 3 * 5; 8
30 = 2 * 3 * 5; 10
50 = 2 * 5 * 5; 12
100 = 2 * 2 * 5 * 5; 14

Notice how when we prime factorize and it goes up by 2. You will also notice that it is the smallest number with such a factorization adding up to that number.

The next number would have a sum of prime factors as 16

possible values
16 = 2 +...+ 2; gives 2^8 =256
16 = 3 + 3 + 5 + 5; gives 3^2 * 5^2 = 225
16 = 2 + 2 + 2 + 5 + 5; gtives 2^3 * 5^2 = 200
and so on.

The smallest such number resulting from such a factorization is 200

Thus 200 is the next term.

Answer 3

A finite sequence of numbers can be attributed to an infinite number of rules. That is, there are an infinite number of sequences that begin with these 8 numbers. Personally, I like the rule:

i) If you want to go from an odd element of the sequence to the next element, like the first to the second, the third to the fourth, the fifth to the sixth, etc., you double;

ii) To get from even elements to odd, try multiplying by 5/2 and then subtracting 5^(n/2-1)...so to get from 2 to 4, you multiply by 5/2 and subtract 5^(2/2-1)=1...to get from 8 to 15, you multiply by 5/2 and subtract 5^(4/2-1)=5...to get from 30 to 50, you multiply by 5/2 and subtract 5^(6/2-1)=25.

Under these rules, the next element of the sequence would be (5/2)*100-5^(8/2-1) = 250-125 = 125. But, as I said, there are an infinite number of sequences that begin with these 8 numbers.

Answer 4

Mathguy is right in saying that there can be infinite sequences starting with these 8 numbers.

And some of the sequences pointed are right.They are the ones pointed by:-
1) mathguy
2) galford_sg
3)noname

but the sequence pointed by volterwd is not right because he says

"Notice how when we prime factorize and it goes up by 2. You will also notice that it is the smallest number with such a factorization adding up to that number."

but take 100=2*2*5*5;14
49=7*7;14

and 49<100

therefore 100 is not the smallest such number and thus that sequence is wrong

Answer 5

i think it could be 154. Here is my reasoning..

The pattern is alternatingly multiply by 2, and then adding alternating terms of the fibonacci sequence. The fibonacci sequence is 1,1,2,3,5,8,13,21,34,55,89, etc

so, 1x2=2
2+2=4
4x2=8
8+(2+5)=15
15x2=30
30+(2+5+13)=50
50x2=100
100+(2+5+13+34)=154
and following this would be 308, then 451 etc
At least this is logical to me. :)

Answer 6

OK im just throwing this out there but i think that the next number would be 100 again. heres why.
8 to 15 is double minus 1
30 to 50 is double minus 10
100 to 100 is double minus 100.
....eh?

Answer 7

well i though that every fourth number was doubled -1, then doubled -2, then doubled -4, and so on and so fourth, but it looks like i'm wrong.... can you beleive some of the answers on here???

I mean if it were as obvious as just doubling i don't think you would need help

Answer 8

Don't you people look at the numbers?! It's NOT doubled each time. I'm working on it, but don't have an answer yet.

Answer 9

Hot crackers!

Those last two entries are starting to use some real brain power. I say they are both correct.

A thumbs up rating to each of ya...

Answer 10

Almost 200, but can't be because 50 is not dopple of 30. Sorry, no idea.