I am really stuck on this problem, I have only gone one step but I have hit a brick wall. I have created two synthons from breaking the C-C bond between the alkene and carbonyl group, but I am unsure on what to do next> I find retrosynthesis very difficult to understand so any tips/suggestions would be very helpful!
The most obvious disconnection here is to heptan-4-one and a formaldehyde equivalent. Mannich reaction looks a strong contender. I would form the enolate with LDA and react with Eschenmoser's salt, work up and then quaternise the product with MeI and eliminate with base to give the product.
Clearly, the approaches are going to be around enolate chemistry, but how to introduce the alkene? My starter for ten would be to start with a conjugated carbonyl. This is either acrolein, an acrylic acid derivative or methyl vinyl ketone. Preferred options would be the latter two. An acrylic ester involves this substrate acting as an electrophile to form the longer chain ketone. Alternatively, methyl vinyl ketone would be the nucleophile to form the longer chain ketone. i. e. As an enolate. This appears to be less problematic.
Maintaining the vinyl ketone in a subsequent step fits nicely with a Morita-Bayliss-Hillmann reaction. However, the electrophile would need to be an alkyl halide as opposed to the traditional aldehyde. This is achievable given the right catalyst.