Its recommended to recite this dua on sighting the crescent of the month of Rajab.
اللَّهُمَّ اهِلَّهُ عَلَيْنَا بِٱلامْنِ وَٱلإِيـمَانِ
O Allah, cause it (i.e. the moon) to appear carrying for us security, faith,
وَٱلسَّلاَمَةِ وَٱلإِسْلاَمِ
safety, and Islam.
رَبِّي وَرَبُّكَ ٱللَّهُ عَزَّ وَجَلَّ
Your and my Lord is Allah, the Glorified and Majestic.
…
It has been also reported that when his eyes fell on the new moon of Rajab, the Holy Prophet (s) used to say the following:
اللَّهُمَّ بَارِكْ لَنَا فِي رَجَبٍ وَشَعْبَانَ
O Allah, (please do) pour out Your blessings upon us in Rajab and Sha`ban.
وَبَلِّغْنَا شَهْرَ رَمَضَانَ
make us reach Ramadhan,
وَاعِنَّا عَلَىٰ ٱلصِّيَامِ
and help us observe fasting,
وَٱلْقِيَامِ
do acts of worship,
وَحِفْظِ ٱللِّسَانِ
suppress our tongues (from saying anything improper),
وَغَضِّ ٱلْبَصَرِ
and cast down our eyes (against what is forbidden for us to look at).
وَلاَ تَجْعَلْ حَظَّنَا مِنْهُ ٱلْجُوعَ وَٱلْعَطَشَ
Do not make our share of Ramadhan only hunger and thirst.