The alkylation of diethyl n-propylmalonate (I) with 1-bromo-2-butyne (II) in the presence of ethanolic NaOEt afforded the dialkyl malonate (III). Subsequent saponification of the ethyl esters of (III) with KOH gave the corresponding malonic acid (IV), which was decarboxylated at 180 C to yield the title compound.

Condensation of pentanoyl chloride (I) with (S)-4-benzyl-2-oxazolidinone (II) in the presence of n-butyllithium afforded the chiral N-acyl oxazolidinone (III). Subsequent asymetric alkylation of (III) with 1-bromo-2-butyne (IV) using LDA as the base produced the alkylated diastereoisomer (V). The chiral auxiliary oxazolidinone was finally removed by hydrolysis with lithium hydroperoxide to afford the required (R)-carboxylic acid.