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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ... -- What's the pattern of this sequence?
2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ... -- What's the pattern of this sequence?
In a contest, such as "Are You Smarter than a Fifth-Grader?", you might be asked, "What's the next number in this sequence? 2, 3, 5". Can anyone figure out the answer?
Comments
OK...
{Highlight to read}
The first one {Highlight to read} is prime numbers; next would be 53.
.
The second {Highlight to read} adds each number to the one that precedes it, so next would be 2584.
Eric
Actually
What number follows five in the sequence in that third line? That's what I meant. You're right about the patterns.
-- Daphne Xu (a page of contents)
IN the third, I’d have to say
IN the third, I’d have to say 8, if the sequence is additive, 2 then 3 is +1, 3 then 5 is +2, 8 would be +3, then 12 for +4, without other info to derive the rule.
So You're Saying...
...there's a reason that someone "smarter than a fifth grader" should choose either 7 or 8 or none of the above? Since the average fifth grader probably hasn't learned the prime number concept yet, I'd say the second.
Another alternative would be 6 (3 is 2+1, 6 is ((2+3)+1)), followed by 11 (5+6),12(5+6+1), 23,24.
Or 10 (2+3+5), followed by 20 (2+3+5+10), but I can't get that one to explain why 3 follows 2.
Eric
1, 1, 2, 3, 5, 8, 13, 21, 34.
1, 1, 2, 3, 5, 8, 13, 21, 34...
Good riddle :)
The first sequence is prime numbers. The second is what is called Fibonacci numbers.
Now, a riddle from me:
Two fishermen went fishing, having decided that they will take equal number of the fish they catch. If they catch an odd number of fish, they will throw out one to make it even.
What is the SMALLEST number of fish each of them could have ended up with?
Can't be Negative.
Zero. I can't think of any way to have a negative number of fish.
-- Daphne Xu (a page of contents)
Why not?
Imagine the slimming effect of a soup from a negative number of fish! :)
Paul Dirac had came up with the answer of a -1 fish per person. However, I don't see a reason why they shouldn't have -2 etc, all the way down to negative infinity.
(I wouldn't recommend a soup made from that, guess why. Actually, I don't even know whether it will be easy or hard to carry this amount of fish home...)
Dirac?
I'd expect him to say that the fishermen already had a negative infinity of negative-mass fish, and then each would looze a certain number.
-- Daphne Xu (a page of contents)
Hey, he came up with the positron!
Not with a negative Higgs boson! :)
Precisely
A full sea of negative-energy electrons is the background and the vacuum. Remove one, you've removed a negative charge and a negative energy. So the hole that's left over is a positron -- positive energy, positive charge.
For those who have trouble understanding this, I might slip my tongue and call the negative-energy sea the "valence band".
-- Daphne Xu (a page of contents)
Why not 9 ?
It could also be the sequence A000051:
a(n) = 2^n + 1 2, 3, 5, 9, 17, 33, 65, 129, 257
Here is a sequence where the next number is 9:
2, 3, 5, 9, 17, 33,
2, 2*2-1=3, 3*2-1=5, 5*2-1=9, ..., S(n) = S(n-1)*2 -1,
EDIT: https://oeis.org/
Your friend
Crash
The Question
I saw that question on a video of a TV show, perhaps "You think you're smarter than a fifth-grader?"
My point was that, given 2, 3, and 5, nothing rules out one sequence over the other -- nothing says that 8 must be right and not 7. And as commentators pointed out, other numbers follow as well, such as in the pattern 2n + 1.
I dislike in general the problem of given a few numbers, what's the next? Potentially any might be next in a pattern. This particular question was egregious in that two possible patterns immediately came to mind. I admit that I didn't think of others, such as 2n + 1 and Sn = 2Sn-1-1 with S0=2. (They're the same, btw.)
-- Daphne Xu (a page of contents)
2,3,5
The Online Encyclopedia of Integer Sequences has 9765 sequences with 2,3,5. Unfortunately, that includes interior sequences, too.
2,3,5,6: 1626 entries. Good sequence: square free numbers greater than 1
2,3,5,7: 2884 entries. The primes
2,3,5,8: 946 entries. Fibonacci numbers
2,3,5,9: 466 entries. 2^n+1
2,3,5,10: 201 entries. Number of nodes of an n-gon with all diagonals drawn.
The real problem is 5th grade
Even lower grade, guess it 2nd grade. If
MAMA + PAPA = CHILDREN
what will be
DOG + CAT = ?
Sequences
DOG + CAT = FIGHT (or maybe FRIENDS?)
This also has more than one solution:
CAT + FISH = ?
Martina
Back to mathematics
mama(4) + papa(4) = children(8),
so
cat(3) + dog(3) = something(6)