It was narrated from Ibn Umar, that:

when the Messenger of Allah performed Tawaf in Hajj and Umarah- as he first arrived (in Makkah), he would hasten in three rounds, and walk (at a regular pace) in four. Then he prayed two Rakahs, then he performed sai between As-Safa and Al-Marwah.

أَخْبَرَنَا قُتَيْبَةُ، قَالَ حَدَّثَنَا يَعْقُوبُ، عَنْ مُوسَى بْنِ عُقْبَةَ، عَنْ نَافِعٍ، عَنِ ابْنِ عُمَرَ، أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ إِذَا طَافَ فِي الْحَجِّ وَالْعُمْرَةِ أَوَّلَ مَا يَقْدَمُ فَإِنَّهُ يَسْعَى ثَلاَثَةَ أَطْوَافٍ وَيَمْشِي أَرْبَعًا ثُمَّ يُصَلِّي سَجْدَتَيْنِ ثُمَّ يَطُوفُ بَيْنَ الصَّفَا وَالْمَرْوَةِ .