The phrase "a week when a" is correct and usable in written English.
It can be used to introduce a specific week that is characterized by a particular event or situation.
Example: "It was a week when a major storm hit the coast, causing widespread damage."
Alternatives: "a week during which" or "a week in which".
She had been there less than a week when a gay couple approached her with the idea of suing to get married.
Gen. Manuel Antonio Noriega had been locked up in a federal prison outside Miami for less than a week when a package arrived with his name on it.
In a week when a 19-year-old has purchased a football club it does not do to patronise youth, but imagine if Tendulkar were English.
The San Bernardino tunnel and pass were closed today for the second time in a week when a truck struck a passenger vehicle.
The weirdness of it feels especially marked in a week when a real flight and 75 real lives were lost in La Unión, Colombia.
This should be said more clearly – it is an omission that stands out particularly in a week when a taboo-breaking publication is being honoured for its courage.
In a week when an American soldier was given no more than a reprimand for smothering an Iraqi general to death, Franklin's 12 1/2 -year sentence was a reminder that this is an administration more horrified by leaks than torture.
Russia and the US agreed to a ceasefire on 9 September, but the truce effectively collapsed after a week when an aid convoy was attacked, killing about 20 people.
After a week when an enormous and spontaneous pilgrimage to pay final respects to Pope John Paul II doubled this city's population, an equally remarkable exodus continued through the day.
Once a week, when an Alitalia flight crew checks in, she wears a long dress and jewelry.
However, the truce effectively collapsed after a week when an aid convoy was bombed on Monday, killing some 20 people.
