Allen Rea, a pastor in Georgia, suggested that the repetition of “found” is a play on words by John.
I love that suggestion. Notice how it brings the verse alive:
“[Andrew] first found his own brother Simon [= Peter], and said to him, ‘We have found the Messiah’ (which is translated, the Christ).”
There are many different ways that John could have reported Andrew going to his brother: Andrew went to his brother… Andrew hurried to his brother… etc.
I searched the major commentaries and only one of them commented on this. J. Ramsey Michaels points out the play on words and suggests that John expects the reader to tie in verse 41 with the Lord’s question in verse 38: “What do you seek?” (pp. 121-22).
The point is that the one who seeks will indeed find. Andrew was seeking to find the Messiah, and he did.
This is a motif in John and in Scripture. All who seek the Lord find Him.
The truth extends beyond regeneration. If we seek, we will find, as long as we are seeking for the right reason. God is a rewarder of those who diligently seek Him (Heb 11:6).
We should constantly seek the Lord. We want to be more and more like Him and the way to do that is by seeking Him in His Word (Rom 12:2; 2 Cor 3:18).
 Editor’s note: The Greek eureka, “found” may look familiar to English readers. From this word, the exclamation Eureka! later derived. It is commonly associated with the California gold rush. The Word in John 1 is a much greater treasure than gold. It is in the written Word that we seek Him. Compare Psalm 19.