Word Chain (?) Bird to Nest

Lloyd is quite fond of math, and likes to incorporate math into almost everything he does. One weekend, the local newspaper printed a Word Chain puzzle, with starting point BIRD and ending with NEST. I had some trouble solving it, and asked Lloyd for help. He told me that he had solved it, and handed me his copy of the puzzle.

When I looked at Lloyd’s “solution”, I didn’t see a chain of words, just a sequence of math operations. Seeing as this is Lloyd, I figured that it really was a solution, but I couldn’t figure out what he was doing.

Here is Lloyd’s solution. Can you reconstruct the actual word chain?

BIRD
-  5408
+    15
+ 17576
+     1
+    26
+158184
+  2704
NEST + 35152

• Would this puzzle benefit from the word-ladder tag too?
– Stiv
Oct 28, 2020 at 16:43
• @Stiv - Yes. When I was typing tags, I got to "word", but it never proposed it, so I didn't know that it existed. Added. Oct 28, 2020 at 16:44
• Aha, yes it's not one of the top 5 most used beginning with 'word' so it won't have shown :)
– Stiv
Oct 28, 2020 at 17:01

Reconstruction:

BIRD, BARD, BARS, CARS, CART, CAST, LAST, LEST, NEST

because

Treat the numbers as increments (or decrements) in alphabetical range, from right to left. E.g. "AZ" + 1 = "BA". You can also think of the words as a number in base-26 with alphabetical digits.

this is evident because

All numbers above 25 in the list are divisible without remainder by either 26, 26*26 or 26*26*26. Since you can only change one letter at a time within a word-ladder, this makes sense.

• Are you really a robot? Oct 28, 2020 at 17:04

It should be noted that I did eventually come up with a solution of my own, and it turns out that it’s shorter than Lloyd’s solution:

BIRD, BARD, CARD (instead of BARS, CARS), CART, CAST, LAST, LEST, NEST