Longest interval between readings of haftarah for Shabbat Rosh Chodesh

Question

When Rosh Chodesh falls on Shabbat, a special haftarah (Isaiah 66) is read.

However, in our fixed calendar certain months can never have Rosh Chodesh fall on Shabbat (Kislev, Sivan). For certain other months, the haftarah for Shabbat Rosh Chodesh is superseded by a different haftarah (Tishrei, Tevet, Adar (II), Nissan, Av).

Thus, the haftarah for Shabbat Rosh Chodesh can only be read for the months of Marcheshvan, Shevat, Adar I, Iyar, Tammuz, Elul.

(I’m aware that there are differing customs regarding Av and Elul; for the purposes of this question assume a community following the custom I have outlined here.)

My question is, what is the longest possible interval in the fixed calendar between readings of this haftarah?

We last read this haftarah in Iyar 5780, and will not do so again until Elul 5782, a gap of 29 months. Is that the longest possible interval?

Bonus: what's the longest interval between readings of the haftarah of Erev Rosh Chodesh?

Answer 1

Since this 29 month gap is longer than 24 months, we can limit our search to gaps that contain at least one complete year without the haftarah.

The only year type with no instances of this Haftara is זח״א Rosh Hashana on Saturday, no 30 Kislev, non-leap year (assuming the practice you mention for Shabbat Rosh Chodesh Av). Such a year is always immediately preceded by this Haftara being read on Rosh Chodesh Iyyar. Such a year is always immediately followed by a year beginning on Tuesday. Non-leap years beginning on Tuesday have this haftarah read for Iyyar while leap years beginning on Tuesday have this haftarah read for Elul (according to the practice you mention) which is longer, and hence is the longest possible gap.

For the reading of "Machar Chodesh", we also find only one year type that doesn't have it read at all, namely בח״ג Rosh Hashana on Monday, no 30 Kislev, non-leap year. Such a year is also always immediately preceded by this Haftara being read on erev Rosh Chodesh Iyyar. Such a year is always immediately followed by a year beginning on Thursday. Years beginning on Thursday always have this haftarah read on erev Rosh Chodesh Kislev. That gap is 5+12+2=19 months. But since that is less than 24 months we have to also search gaps that don't include an entire year without the haftarah.

Indeed we find in years זח״א beginning on Saturday, no 30 Kislev, non-leap year this haftarah is read for Marcheshvan. As above, such a year is always immediately followed by a year beginning on Tuesday. Non-leap years beginning on Tuesday have this haftarah read for Sivan while leap years beginning on Tuesday have this haftarah read for Iyyar which are both 8 months into the year. Hence we have a gap of 11+8=19 months. I believe that is the longest possible gap.