This paper presents an algorithm for real-time detection of the heart rate measured on a person's wrist using a wearable device with a photoplethysmographic (PPG) sensor and accelerometer. The proposed algorithm consists of an appropriately trained LSTM network and the Time-Domain Heart Rate (TDHR) algorithm for peak detection in the PPG waveform. The Long Short-Term Memory (LSTM) network uses the signals from the accelerometer to improve the shape of the PPG input signal in a time domain that is distorted by body movements. Multiple variants of the LSTM network have been evaluated, including taking their complexity and computational cost into consideration. Adding the LSTM network caused additional computational effort, but the performance results of the whole algorithm are much better, outperforming the other algorithms from the literature.