Prime numbers?

Level 2

Find the next term in this sequence.

2 , 3 , 5 , 7 , 2 , 4 , 8 , 10 , 5 , 11 , 4 , 10 , ? 2,3,5,7,2,4,8,10,5,11,4,10, ?


The answer is 5.

Archit Boobna by Archit Boobna , 20, India

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1 solution

TheOnly Caosun
Jun 9, 2015

The title of the question suggest that the sequence has something to do with prime numbers.

2, 3, 5, 7 are prime numbers, and the following prime numbers are 11, 13, 17, and 19.

Comparing 11, 13, 17, and 19 to 2, 4, 8, 10, there is a difference of 9. Next, comparing primes 23 and 29 to 5 and 11 in the sequence yields a difference of 18. Next, comparing primes 31 to 37 to numbers 4 and 10 yield a difference of 27.

So since the next prime number is 41, and the difference should be 36, the number is 5.

This is my first explanation so give me some tips. I realize this is not a systematic explanation, I just guess and checked.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Wow this is a great observation! Actually this has happened because of the magical divisibility rule of 9. The simplest answer to this question is that it is the sequence of the sum of digits of primes.

Compare 11, 13, 17, 19 to 2, 4, 8, 10.

2 is the digital sum of 11. 4 is the digital sum of 13.

And so on.

This was the simple rule! Thanks!

Archit Boobna - 6 years ago

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