For further research I have gone back and collected many of the verses found since the beginning of the book of John relating to key words and concepts that are emerging as important here. Following is a list of key verses relating to the idea of coming and receiving.
Come
The next day he saw Jesus coming to him and said, "Behold, the Lamb of God who takes away the sin of the world! (John 1:29)
He said to them, "Come, and you will see." So they came and saw where He was staying; and they stayed with Him that day, for it was about the tenth hour. (1:39)
He found first his own brother Simon and said to him, "We have found the Messiah" (which translated means Christ). He brought him to Jesus. Jesus looked at him and said, "You are Simon the son of John; you shall be called Cephas" (which is translated Peter). (1:41-42)
The next day He purposed to go into Galilee, and He found Philip. And Jesus said to him, "Follow Me." (1:43)
Nathanael said to him, "Can any good thing come out of Nazareth?" Philip said to him, "Come and see." (1:46)
Now there was a man of the Pharisees, named Nicodemus, a ruler of the Jews; this man came to Jesus by night and said to Him, "Rabbi, we know that You have come from God as a teacher; for no one can do these signs that You do unless God is with him." (3:1-2)
This is the judgment, that the Light has come into the world, and men loved the darkness rather than the Light, for their deeds were evil. For everyone who does evil hates the Light, and does not come to the Light for fear that his deeds will be exposed. But he who practices the truth comes to the Light, so that his deeds may be manifested as having been wrought in God. (3:19-21)
John also was baptizing in Aenon near Salim, because there was much water there; and people were coming and were being baptized. (3:23)
And they came to John and said to him, "Rabbi, He who was with you beyond the Jordan, to whom you have testified, behold, He is baptizing and all are coming to Him." (3:26)
"Come, see a man who told me all the things that I have done; this is not the Christ, is it?" They went out of the city, and were coming to Him. (4:29-30)
So when the Samaritans came to Jesus, they were asking Him to stay with them; and He stayed there two days. (4:40)
The sick man answered Him, "Sir, I have no man to put me into the pool when the water is stirred up, but while I am coming, another steps down before me." (5:7)
Do not marvel at this; for an hour is coming, in which all who are in the tombs will hear His voice, and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment. (5:28-29)
You are unwilling to come to Me so that you may have life. (5:40)
Receive (very close to believe but those are not included in this list)
He came to His own, and those who were His own did not receive Him. But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name. (John 1:11-12)
For of His fullness we have all received, and grace upon grace. For the Law was given through Moses; grace and truth were realized through Jesus Christ. (1:16-17)
Truly, truly, I say to you, we speak of what we know and testify of what we have seen, and you do not accept our testimony. (3:11)
John answered and said, "A man can receive nothing unless it has been given him from heaven." (3:27)
What He has seen and heard, of that He testifies; and no one receives His testimony. He who has received His testimony has set his seal to this, that God is true. For He whom God has sent speaks the words of God; for He gives the Spirit without measure. (3:32-34)
Jesus answered and said to her, "If you knew the gift of God, and who it is who says to you, 'Give Me a drink,' you would have asked Him, and He would have given you living water." (John 4:10)
Already he who reaps is receiving wages and is gathering fruit for life eternal; so that he who sows and he who reaps may rejoice together. (4:36)
So when the Samaritans came to Jesus, they were asking Him to stay with them; and He stayed there two days. (4:40)
But the testimony which I receive is not from man, but I say these things so that you may be saved. (5:34)
I do not receive glory from men. (5:41)
I have come in My Father's name, and you do not receive Me; if another comes in his own name, you will receive him. How can you believe, when you receive glory from one another and you do not seek the glory that is from the one and only God? (5:43-44)
I can see there is a great deal of instruction for me in viewing these verses together like this. I hope to take more time to review them thoughtfully.