I found two 10-letter (4 disctinct) words having this property: sereneness sleeveless And a bunch of 6-letter (3 distinct) words: Assisi Canaan Mennen acacia assays banana baobab bedded cocoon deemed doodad eddied eerier effete heeded horror hubbub inning lessee mammal mammas messes needed papaya peeped peeper pepped pepper pippin powwow reefer revere rococo salsas seeded senses settee tattoo teeter teethe titbit wedded weeded Tom Dan Asimov writes:
Speaking of word oddities, Ararat (or tarara, as in "tarara boom-de-ay") has one T, two R's, and three A's.
Is there any other word having its letter counts form an arithmetic sequence of at least three positive terms?
—Dan