perplexus.info :: Sequences : Check this sequence

Check this sequence (Posted on 2020-08-24)

6,10,14,15,21,22,....ad inf

This sequence consists of products of two distinct primes.

1. What is the 1st appearance of 3 successive numbers?
2. How many triplets like n, n+1, n+2 are there below 2000?
3. Prove that 4 numbers in a succession cannot appear in this sequence.

No Solution Yet Submitted by Ady TZIDON

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Part 3 proof (spoiler) | Comment 2 of 3 |

Given any set of 4 consecutive integers, one of them must be divisible by 4. This cannot be the product of two primes (unless it is 4 itself, and 4 is not part of the sequence).

Posted by Steve Herman on 2020-08-24 10:04:57

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