You can count on Sergeant Sequence

Question

"Ah, Sequence, there you are," said the Chief Investigator as Sergeant Sequence entered the briefing room. "Your man Patrick Terne is on the move again, and we need your help to track him down."

"Where's he been this time?" asked the Sergeant, cradling his morning coffee.

"All over - a lot of time in Asia, then Europe, Russia, and last we heard he's in Virginia."

"The US?"

"No, South Africa, actually - but we've had a tip-off that he's heading for the US next, specifically one of the fifty state capitals... We're just not sure which. Cast your eye over this..."

Sergeant Sequence took a look at the list of locations where his nemesis had been spotted and took a sip of his coffee...

1. Shanghai, China
2. Beijing, China
3. Bukittinggi, Indonesia
4. Kyiv, Ukraine
5. Yerevan, Armenia
6. Reykjavik, Iceland
7. Novosibirsk, Russia
8. Virginia, South Africa
9. Unknown - one of the 50 US state capitals...

After a couple of seconds, Sequence laughed. "I know exactly where he's going, sir." He wrote a city on the whiteboard. The CI smiled.

"I can always count on you!" he said, warmly.

TASK: Identify the pattern behind the sequence of cities and the US state capital that Terne will be visiting next.

Answer 1

The city Terne will visit next is:

PHOENIX, Arizona, USA

The break-in:

There are a lot of repeated letters in most of the cities, and quite a few ABA patterns, but KYIV eliminates any "double letter" or "letter patterns" from consideration...there's just not enough there there.

But then...there are a lot of repeated I's. And there are quite a few V's, too. That makes you think...Roman numerals. Add the title: "you can COUNT on Sgt. Sequence", and you're there.

The data:

Remove all of the letters that are not Roman digits (I,V,X,L,C,D,M) from each city and you get:

1. shanghaI → I
2. beIjIng → II
3. bukIttInggI → III
4. kyIV → IV
5. yereVan → V
6. reykjaVIk → VI
7. noVosIbIrsk → VII
8. VIrgInIa → VIII

The answer:

So the next city Terne will visit must be a US capital with IX=9 in it. Full disclosure: I was literally in PHOENIX last week on vacation, and I still had to look it up, because I'm old and dumb. But either way it made sense to look at a list to see that it was the only one. Anyway, the only US capital with an X in it is in fact PHOENIX and it transforms via phoenIX → IX.

Conjecture:

If we miss Terne in the States, he'll be in Luxembourg next! OR NOT...the M, the M! Must be sfaX!