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Which number comes next in the sequence?

2, 7, 19, 47, 83, ___


Please remember to explain your reasoning and put your answer and reasoning behind spoilers. (Do >! and then your text to put one)

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  • $\begingroup$ leastcommonmultiple.net/lcm-of-14-19-47-and-83 $\endgroup$
    – Richard
    Commented Apr 19, 2015 at 19:16
  • $\begingroup$ Hmm... Yeah... What's Your Point? $\endgroup$ Commented Apr 19, 2015 at 19:18
  • $\begingroup$ No point, just an observation. $\endgroup$
    – Richard
    Commented Apr 19, 2015 at 19:19
  • $\begingroup$ Oh, well okay then $\endgroup$ Commented Apr 19, 2015 at 19:20
  • $\begingroup$ They're all primes, that's what you're trying to say, perhaps $\endgroup$
    – leoll2
    Commented Apr 19, 2015 at 19:28

3 Answers 3

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This looks like a sequence extracted from the series of prime numbers. The next number could be:

139 which is the $34^{th}$ prime number.

The sequence to select prime numbers is $n^2-floor((n-1)/2)$

Sequence

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  • $\begingroup$ It's surprisingly close to the prime numbers at Fibonacci indices - 3, 5, 8, 13, 21, 34 $\endgroup$
    – mdc32
    Commented Apr 20, 2015 at 1:35
  • $\begingroup$ @mdc32 - Yes, that would also work by using an adjustment function of -2,-1, 0,+2,+2 which would be a little more complex. $\endgroup$
    – Len
    Commented Apr 20, 2015 at 1:45
5
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Assuming the commas are superfluous; the numbers could relate to

This marker on the Neanderthal genome; http://neandertal.ensemblgenomes.org/Homo_sapiens/Location/Marker?r=16:26994784-27194783. The next number would therefore be 16.

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  • $\begingroup$ Sorry, that's not it, but I will upvote for the effort. $\endgroup$ Commented Apr 19, 2015 at 19:24
5
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The Next Number's will be:

139,199

The Reason is:

The Sequence is following +1, +3,+1,+3,......

The Prime number sequence is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,..

The logic is as following:

2 after 2 prime numbers, it is 7
7 after 3=>(2+1) prime numbers, it is 19
19 after 6=>(3+3) prime numbers, it is 47
47 after 7=>(6+1) prime numbers, it is 83
83 after 10=>(7+3) prime numbers, it is 139 and so on...

Finally:

2,7,19,47,83,139

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