Acts 13:42-48 (ESV)
42 As they went out, the people begged that these things might be told them the next Sabbath. 43 And after the meeting of the synagogue broke up, many Jews and devout converts to Judaism followed Paul and Barnabas, who, as they spoke with them, urged them to continue in the grace of God.
44 The next Sabbath almost the whole city gathered to hear the word of the Lord. 45 But when the Jews saw the crowds, they were filled with jealousy and began to contradict what was spoken by Paul, reviling him. 46 And Paul and Barnabas spoke out boldly, saying, “It was necessary that the word of God be spoken first to you. Since you thrust it aside and judge yourselves unworthy of eternal life, behold, we are turning to the Gentiles. 47 For so the Lord has commanded us, saying,
“‘I have made you a light for the Gentiles, that you may bring salvation to the ends of the earth.’”
48 And when the Gentiles heard this, they began rejoicing and glorifying the word of the Lord, and as many as were appointed to eternal life believed.
Acts 15:19-21 (ESV)
19 Therefore my judgment is that we should not trouble those of the Gentiles who turn to God, 20 but should write to them to abstain from the things polluted by idols, and from sexual immorality, and from what has been strangled, and from blood. 21 For from ancient generations Moses has had in every city those who proclaim him, for he is read every Sabbath in the synagogues.”
Acts 16:11-14 (ESV)
11 So, setting sail from Troas, we made a direct voyage to Samothrace, and the following day to Neapolis, 12 and from there to Philippi, which is a leading city of the district of Macedonia and a Roman colony. We remained in this city some days. 13 And on the Sabbath day we went outside the gate to the riverside, where we supposed there was a place of prayer, and we sat down and spoke to the women who had come together. 14 One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul.
Acts 17:1-4 (ESV)
Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where there was a synagogue of the Jews. 2 And Paul went in, as was his custom, and on three Sabbath days he reasoned with them from the Scriptures, 3 explaining and proving that it was necessary for the Christ to suffer and to rise from the dead, and saying, “This Jesus, whom I proclaim to you, is the Christ.” 4 And some of them were persuaded and joined Paul and Silas, as did a great many of the devout Greeks and not a few of the leading women.
Acts 18:4 (ESV)
4 And he reasoned in the synagogue every Sabbath, and tried to persuade Jews and Greeks.
I've seen these passages cited many times as evidence that the Gentiles in the New Covenant are to keep the Sabbath, just like the Jews.
At face value, I can agree that these passages are clear evidence that the Gentiles attended synagogues on Sabbath, there is no question about that. However, can we go one step further interpretatively and assert that they were actually keeping the Sabbath commandment and, by reasoning inductively, that these passages of Acts are evidence that Christian Gentiles in general are to keep the Sabbath?