Finding maximum number of consecutive days

	a	b	c
2	4/3/2019	3	b2: {=max(frequency(if(a3:a13 = a2:a12 + 1, row(a3:a13)), if(a3:a13 <> a2:a12 + 1, row(a3:a13)))) + 1}
3	4/5/2019
4	4/7/2019
5	4/10/2019
6	4/12/2019
7	4/14/2019
8	4/17/2019
9	4/19/2019
10	4/20/2019
11	4/21/2019
12	4/24/2019
13	4/28/2019

If dates starts in A1, put into B1:

Formula:

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accept with Ctrl+Shift+Enter.

You can't type in the curly braces in an array formula.

Paste the formula in the formula bar, press and hold the Ctrl and Shift keys, then press Enter. That will make them appear.

Both works.
From your last attachment:
in B2 (mine formula) has not been accepted with Ctrl+Shift+Enter, accept with CSE and it gives you 2.
in F2 (shg formula) curly brackets probably added manually, delete them (at start / at end) accept with CSE (as above) and it gives you 2.