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No First-Hand-Neighbors & Second-Hand-Neighbors!!!

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Create the shortest possible sequence such that no number is next to its first-hand or second-hand neighbors (e.g., the number 3 cannot be next to numbers 1, 2, 4, or 5, which are first- and second- neighbors).

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3,6,2,5,1,4

is a 5 sequence possible?

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3,6,2,5,1,4

is a 5 sequence possible?
No as there would be a number that could not be beside any other. For example in a sequence of numbers 1-5 the number 3 could not be beside any other number making a run of 5 (or less) impossible.
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1

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i should have been more clear in the op, the sequence must start at 1 and go to some n greater than 1 (consecutively).

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