Context : The saturated n -propyl cyanide was recently detected in Sagittarius B2 ( N ) . The next larger unbranched alkyl cyanide is n -butyl cyanide . Aims : We provide accurate rest frequency predictions beyond the millimeter wave range to search for this molecule in the Galactic center source Sagittarius B2 ( N ) and facilitate its detection in space . Methods : We investigated the laboratory rotational spectrum of n -butyl cyanide between 75 GHz and 348 GHz . We searched for emission lines produced by the molecule in our sensitive IRAM 30 m molecular line survey of Sagittarius B2 ( N ) . Results : We identified more than one thousand rotational transitions in the laboratory for each of the three conformers for which limited data had been obtained previously in a molecular beam microwave study . The quantum number range was greatly extended to J \approx 120 or more and K _ { a } > 35 , resulting in accurate spectroscopic parameters and accurate rest frequency calculations up to about 500 GHz for strong to moderately weak transitions of the two lower energy conformers . Upper limits to the column densities of N \leq 3 \times 10 ^ { 15 } cm ^ { -2 } and 8 \times 10 ^ { 15 } cm ^ { -2 } were derived towards Sagittarius B2 ( N ) for the two lower energy conformers , anti - anti and gauche - anti , respectively . Conclusions : Our present data will be helpful for identifying n -butyl cyanide at millimeter or longer wavelengths with radio telescope arrays such as ALMA , NOEMA , or EVLA . In particular , its detection in Sagittarius B2 ( N ) with ALMA seems feasible .