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 صلى الله عليه وسلم كَانَ إِذَا طَافَ فِي الْحَجِّ وَالْعُمْرَةِ أَوَّلَ مَا يَقْدَمُ فَإِنَّهُ يَسْعَى ثَلاَثَةَ أَطْوَافٍ وَيَمْشِي أَرْبَعًا ثُمَّ يُصَلِّي سَجْدَتَيْنِ ثُمَّ يَطُوفُ بَيْنَ الصَّفَا وَالْمَرْوَةِ ‏.‏