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In the following sentence:
调查显示，32%的海外民众认为中国是对世界经济影响最大的国家。与5年前相比翻了一番。
一番 might mean "one time" (at least my dictionary on macOS says "一倍" while Pleco only lists "one kind"). However, 翻 I believe means "double" as a verb here.
So I feel that the sentence is contradictionary... At least from the context, the influence of China would be "doubled". But then what is the meaning of 一番 here?
翻（了）n番 is common phrase, meaning 2^n. For example, 翻一番 = 2, 翻两番 = 4， ....
But the interesting phrase is 翻n倍. Some would take 翻n倍 = 翻n番, and some would take 翻n倍 = 1*n, and some take 翻n倍 = 1*(n+1). For example, 50翻3倍 could be 150, 400 or 200. This is really a moot point. Personally, I would take 翻n倍 = 1*(n+1) and 50翻3倍 would be 200.
I found that Pleco has the entry. The entry is on neither 一番 or 番 but 翻番.
According to the dictionary:
- increase by a specified number of times
And the example sentences are:
翻两番 // quadruple
十年内学生人数翻了一番。 // The school's enrollment doubled in ten years.
Your intuition is correct:
新招聘信息翻了一番。
New job ads doubled.
结果日产量翻了一番。
As a result output doubled.
与5年前相比翻了一番。 (This percentage) compared with 5 years earlier has doubled.
The correct phrasing should be 与5年前相比翻了一翻. The first 翻 is the verb, the second 翻 is a verb classifier.
More example
斬一斬 (chop one chop = take one chop /chop once)
看一看 (look one look = take one look/ look once)
翻一翻 (flip one flip = take one flip/ flip once = doubling once)
A measure word (e.g. 一, 幾) followed by a 'verb classifier' describe how many times the action verb occurred. If it wrote "翻了幾翻", then it would mean "flipped a few flips" = "doubled the original number a few times"
double up
翻了一翻 actually means "翻(倍)了一翻"
