Construct a pure function containing built-in 'Sequence'

Question

I guessed the output for

 (Sequence[#, 7]&)[3]

should be

 Sequence[3,7]

But my guess was wrong. See the screenshot:

And I tried to construct such function as pure-function, but failed.

A workaround (not as pure-function) is Seq[x_] := Sequence[x, 7]

Q1) Why does the code Sequence[#, 7]&)[3] fail ?
Q2) Is it possible to construct such function as a pure-function ?

Answer 1

It fails because Sequence releases the hold when subjected to the syntax &, as & is effectively the same as Function. For example, the following two are semantically equivalent:

#^2 &
Function[#^2]

and now replace #^2 with Sequence[#, 7]:

Function[Sequence[#, 7]]

by which Sequence automatically releases the hold as it's supposed to, turning the expression into Function[#1, 7] or equivalently Function[Slot[1], 7], a syntax error for Function. A workaround that I could think of is just using Hold instead of Sequence and releasing it later when evaluating:

Hold[#, 7] &[3]
(* Hold[3, 7] *)

f[Hold[#, 7] &[3]] // ReleaseHold
(* f[3, 7] *)

Answer 2

##& is functionally equivalent to Sequence in most cases, and does the job here.

So long as the argument is not evaluated, ##&[...] will remain unexpanded, even under heads that do not have SequenceHold:

Answer 3

If your Sequence is intended to be used within an enclosing List, then you could use Splice.

Splice[{#, 7}] &

(*for example...*)
Splice[{#, 7}] &[3]
(*...returns Splice[{3, 7}]*)

(*...and...*)
{1, (Splice[{#, 7}] &)[8], 3}
(*...returns {1, 8, 7, 3}*)

Alternatively, you just need to delay the application of Sequence (as pointed out in the comment by kglr).

Sequence @@ {#, 7} &

(*for example...*)
Sequence @@ {#, 7} &[8]
(*...returns Sequence[8, 7]*)

Answer 4

An alternative way would be to use Construct:

(Construct[Sequence,#,7]&)[3]

(* Sequence[3, 7] *)