What Is the Next Number in Holmes' Curious Sequence?

[peteb]

In Sir Arthur Conan Doyle's Sherlock Holmes story "Silver Blaze" we find:

"Is there any other point to which you wish to draw my attention?"
"To the curious incident of the dog in the nighttime."
"The dog did nothing in th nighttime."
"That was the curious incident," remarked Sherlock Holmes

*****

Here is a series:

1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44.

Having taken Holmes' point on board, what is the next number in the sequence?


Pete B

 

[LAF]

The answer is:

Spoiler

46,47,49,61,77

 

[peteb]

That's correct. For the benefit of the others, would you care to explain how you arrived at that answer?

Pete B

 

[Jonathan Scott]

I saw there were no multiples of 3 or 5 but it took me longer to realize why some numbers such as 13, 23, 34 and 59 aren't there, which is that there are no digits 3 or 5 either. Even then, I was a bit uncertain and Googled it, and confirmed that appears to be the answer.

 

[LAF]

As Jonathan said, there is no 3 and 5 multiples and no 3 and 5 digits either.

 

[ashishsinghal]

Where was the dog?

 

[LAF]

Where was the dog?

The dog was resting at home. It was 35 years old. :)