Allonsy!
Sherlock does not solve every case. Sure, he gets a large majority of them, but every once in a while there's one that goes unsolved.
Eight days ago, Sherlock didn't solve an important case. People died, someone got away, and Sherlock's brain sort of shut down. In the cab going home he was silent, he went to bed silently, he woke up silently, and as soon as he got out of bed, he went to the sofa and sulked.
At this point, John knows how to deal. Until there's another case, Sherlock likes to watch Doctor Who. Doctor Who helps his brain, sort of, restart. It helps him recharge. It keeps him from beating himself up over it.
For eight days, Sherlock's done nothing but watch Doctor Who. John is going crazy waiting for a new case, but he can't imagine how Sherlock feels. All he does is sit there all day.
Finally Lestrade calls John. There's a body with a missing head leaking blue ink and it smells like roses. Of course this is right up Sherlock's alley.
John gets Sherlock to get ready and turns off Doctor Who. They leave off on season 4, and Sherlock gleefully goes to the case.
Sherlock dashes around the crime scene like nothing is wrong. He's well energized and his deductions are spot on. John watches in amazement and offers words of encouragement.
Sherlock spots trickles of the blue ink far away from the body. He nearly hops with excitement and calls after John, "Allons-y!"
Lestrade looks at John. "Did he just say—"
John buries his face in his hand. "Yes."
Lestrade is silent for a minute, then asks, "Did you break him?"
John sighs. "Doctor Who is his remedy. He watches it and refuels."
"John!" Sherlock calls.
"What?"
"I require your assistance! I called for you! Didn't you hear me?"
"Oh, I heard you," John says.
Lestrade begins to laugh. "You're his little companion."
"I am not!" John pouts.
"You are! You follow him around and do as he asks! You're his little companion!"
"I'm going to kick your little companion if you don't stop calling me 'little'," John warns.
Lestrade laughs harder.
"John!" Sherlock shouts.
Lestrade continues laughing as he walks towards Sherlock. He glances back at John and John isn't moving. "Didn't you hear him?" Lestrade calls to John. "Allons-y!"
*This prompt was given by hpgleek713 and it was for Allons-y! which is a major thing in the DW fandom, of course, and I have a headcanon that Sherlock loves Doctor Who. Because really…who doesn't?!