Question 962850: 0,3,2,2,4,4,6,6,9,9,_,
Find the next number in the sequence.
Hint: RMTK
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
The next term is the 11th term, so we only need to look at the
odd terms.
The odd numbered terms are the number of primes less than (n+1)²/4
term #1 = 0 = the number of primes less than (1+1)²/4=1.
term #3 = 2 = the number of primes less than (3+1)²/4=4. They are 2,3
term #5 = 4 = the number of primes less than (5+1)²/4=9. They are 2,3,5,7
term #7 = 6 = the number of primes less than (7+1)²/4=16. They are 2,3,5,7,11,13
term #9 = 9 = the number of primes less than (9+1)²/4²=25. They are 2,3,5,7,11,13,17,19,23
term #1 = 11 = the number of primes less than [(11+1)/2]²=36. They are 2,3,5,7,11,13,17,19,23,29,31
So the answer is 11.
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You don't need the pattern for the even terms.
But let's find it anyway:
The even umbered terms go 3,2,4,6,9,6,8,12
3,2, each times 1, gives 3,2
2,3, each times 2, gives 4,6
3,2, each times 3, gives 9,6
2,3, each times 4, gives 8,12
3,2, eact times 5, gives 15,10
Edwin
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