Luke started accompanying Paul beginning in Acts 16

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It must escape many peoples notice that Luke was following the twelve apostles in Jerusalem during most of his writing. The book of the Acts of the apostles begins as a continuation of the epistle bearing his name. Luke says so in the first verse of Acts:

Acts 1:1 (KJV)
(1:1) The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach,

But, in Acts 16, we can see that the personal pronouns suddenly change:

Acts 16:6-15 (KJV)
(16:6) Now when they had gone throughout Phrygia and the region of Galatia, and were forbidden of the Holy Ghost to preach the word in Asia, (16:7) After they were come to Mysia, they assayed to go into Bithynia: but the Spirit suffered them not. (16:8) And they passing by Mysia came down to Troas. (16:9) And a vision appeared to Paul in the night; There stood a man of Macedonia, and prayed him, saying, Come over into Macedonia, and help us. (16:10) And after he had seen the vision, immediately we endeavoured to go into Macedonia, assuredly gathering that the Lord had called us for to preach the gospel unto them. (16:11) Therefore loosing from Troas, we came with a straight course to Samothracia, and the next [day] to Neapolis; (16:12) And from thence to Philippi, which is the chief city of that part of Macedonia, [and] a colony: and we were in that city abiding certain days. (16:13) And on the sabbath we went out of the city by a river side, where prayer was wont to be made; and we sat down, and spake unto the women which resorted [thither]. (16:14) And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard [us]: whose heart the Lord opened, that she attended unto the things which were spoken of Paul. (16:15) And when she was baptized, and her household, she besought [us], saying, If ye have judged me to be faithful to the Lord, come into my house, and abide [there]. And she constrained us.

It's impossible to miss the fact that Luke no longer accompanied the twelve but now accompanied Paul and those with him.

From "they" and "them" to "we" and "us"... marked clearly in Acts 16.

It is also notable that we do not see Peter mentioned in Acts from chapter 16 to the end.