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What are the next 3 terms in the following finite sequence?

19, 43, 59, 23, 79, 83, 109, 463, 569, 263, ?, ?, ?

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  • $\begingroup$ The deleted answer is almost correct... $\endgroup$ Dec 10, 2023 at 22:24
  • $\begingroup$ post it again please and I will tell you what is missing $\endgroup$ Dec 11, 2023 at 10:30

1 Answer 1

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The answer is

769, 863, 1009

The idea is that the sequence goes all the way to ten after adding the 6s in the second digit slot.

The ideas behind the pattern is that the last digit alternates between 9 and 3 per number. Then the first digits alternates between, 1,4,5,2,7,8 per number and each time this latter sequence repeats one inserts a 6 in the 2 digit slot and displace all above it up a slot. But for the 1 you put a 0.

The sequence ends on 46663 since they all have to be prime numbers in the sequence but you cannot add any numbers to the sequence without adding the previous number generated by the pattern even if it doesn’t belong in the sequence. So since you can’t include 56669 any other numbers cannot be place in the sequence following these rules. The next number generated after 46663 would be 56669 a non prime.

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  • $\begingroup$ This is close, but not my pattern. The first two numbers are correct, but not the third one. $\endgroup$ Dec 12, 2023 at 12:40

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