# What is a Frightful Number™?

This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

An entry into the 20th fortnightly topic challenge.

# Main puzzle:

If a number conforms to a certain rule, I call it a Frightful Number™. Use the following examples to find the rule:

Here is a CSV:

Frightful Numbers™,Non-Frightful Numbers™
15,23
427,487
729,512
2016,6210
13579,24680
492717,638424
1837591,4295354
43728161,15594260
1010101010,1001001001
1738629405,7293548016
46819275183,62571139572
92729092729,72627472627
7070707070707,4141414141414


The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a Frightful Number™ on its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.

These are not the only examples of Frightful Numbers™ (or non-Frightful Numbers™), more can be found.

Hints:

1. The title of the puzzle is a synonym for the required property - this is to ensure that it isn't too easy (it would be if I gave you the word)

2. The whole number being Frightful™ is a property of its parts

# Bonus Puzzle!

(For those like Deusovi who don't find normal What is a Number™ puzzles interesting enough)

Frightful Numbers™ and Not Frightful Numbers™ have a real-world application.

Your challenge is (assuming you have found an answer to the main puzzle) to find what this could be ... It's not too hard to think of if you have the correct answer.

I think I might have missed the Halloween boat on this one... Oh well...

Here's hoping I don't make another silly mistake like last time!

• What's wrong with the question, @downvoter? – boboquack Nov 23 '16 at 7:17
• Wasn't me who downvoted - I don't particularly like "What is a _____ Number™" clues since there aren't as many interesting non-obscure properties to exploit with numbers instead of words. I suspect the downvoter felt the same way. – Deusovi Nov 23 '16 at 7:31
• @Deusovi Well then here's hoping that it is interesting enough for you. It's definitely not very obscure, but does require lateral thinking (not enough though to warrant that tag). – boboquack Nov 23 '16 at 7:34
• Are all numbers either Frightful (tm) or Not Frightful (tm), or are some numbers neither? (The names suggest that Not Frightful = not Frightful, but the comment about real-world applications suggests maybe both are names of special categories of number.) – Gareth McCaughan Nov 23 '16 at 17:33
• oh i know this one! ... because 7 8 9! – monoRed Nov 24 '16 at 21:10

Frightful Numbers™ are numbers that don't contain consecutive digits that are either the same or directly adjacent on a telephone keypad:
123
456
789
--0 (0 should be aligned directly below the 8)
They are called Frightful Numbers™ because they are afraid of their neighbors/constantly on the run?? (not sure about this yet)

Examples:

One example to show the non-connectedness of the frightful numbers I've tried to draw here: (this is for the number 1738629405, consecutive lines have been giving alternating colors, red-blue-red-...)

The counterexamples are a lot easier to "show", as I've tried to do here below: (left is the not-frightful number itself, right is where it "connects"):
23 (2-3)
487 (8-7)
512 (1-2)
6210 (2-1)
24680 (8-0)
638424 (6-3)
4295354 (5-4)
15594260 (5-5)
1001001001 (0-0)
7293548016 (5-4 and 8-0)
62571139572 (1-1 and 2-5)
72627472627 (7-4 and 4-7)
4141414141414 (4-1 and 1-4)