What logic is followed below to get the numbers for the months?

MARCH = 3142

APRIL = 1232

MAY = 1121

JUNE = 1220

JULY = ?

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    $\begingroup$ Is the last digit for April definitely 2, not 3? $\endgroup$ – Stiv Nov 30 '20 at 0:08
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    $\begingroup$ @Stiv agreed I think it should be three, I know them all except the first number now :P $\endgroup$ – Beastly Gerbil Nov 30 '20 at 0:09
  • $\begingroup$ Is this your own puzzle? If not, please add source. $\endgroup$ – Pilot Nov 30 '20 at 0:57
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    $\begingroup$ @user71981 DrD is one of our most prolific original puzzle setters on PSE - you probably don't need to question the source on puzzles bearing their name unless you have actually found it elsewhere! :) $\endgroup$ – Stiv Nov 30 '20 at 7:20
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    $\begingroup$ @Stiv I truly appreciate your comment above. I will most certainly give attributions if it is not my puzzle-- I have done so previously. And hexomino has the answer so the last number for April is correct. $\endgroup$ – DrD Nov 30 '20 at 12:51

Thanks to Prim3numbah for the suggestion on the last digit, I think it might be

JULY = 1131

First digit

If we look at the number of days in each month then the first digit represents the absolute difference between the number of days in the month and the number of days in the previous month when they next occur.

For example, the next occurrence of MARCH has 31 days which is 3 more than the next time we see FEBRUARY (28 days). APRIL has 1 less than MARCH and JULY will have 1 more than JUNE.

Second digit

This is just the number of vowels in the name of the month

Third digit

This is the number of consonants in the name of the month

Last digit (solved by Prim3numbah)

This is the number of letters in the name of the month which are also Roman numerals.

Original guess for last digit

0 - number of letters which are A or R (topologically equivalent to A).

Easter Egg (spotted by Stiv)

The digits for MARCH seem to represent a decimal approximation for $\pi \approx 3.142$ and Pi Day occurs in March.

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    $\begingroup$ Aaah was just about to send :) But the last digit is probably the number of rot13(ebzna ahzrenyf, fb fubhyq or bar) $\endgroup$ – Prim3numbah Nov 30 '20 at 10:19
  • $\begingroup$ D'oh! Facepalm for not getting my finger on digit-1 (you can probably just go for 'in general' rather than 'when they next occur'). And yes, my digits 2-4 were exactly as you specify above. Though I really like the suggestion by @Prim3numbah in the comment above - especially as DrD tends to have a fondness for those! +1 for a fully thought-through and reasoned solution before posting. $\endgroup$ – Stiv Nov 30 '20 at 10:22
  • $\begingroup$ (Also I think DrD's design choice for this puzzle is evident if you pop a decimal point between the first and second digits of March's number... Just a little Easter Egg there...) $\endgroup$ – Stiv Nov 30 '20 at 10:24
  • $\begingroup$ @Prim3numbah Aaah, that is a good suggestion actually. $\endgroup$ – hexomino Nov 30 '20 at 10:24
  • $\begingroup$ @Stiv Thanks, I've added your Easter Egg spot. $\endgroup$ – hexomino Nov 30 '20 at 10:29

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