An autogram is a sentence that describes itself in the sense of providing an inventory of its own characters. They were invented by Lee Sallows, who also coined the word ‘autogram’. An essential feature is the use of full cardinal number names such as “one”, “two”, etc., in recording character counts. Autograms are also called ‘self-enumerating’ or ‘self-documenting’ sentences.
The first autogram to be published was composed by Lee Sallows in 1982 and appeared in Douglas Hofstadter's Metamagical Themas column in Scientific American. (Lee Sallows is possibly more well know for his work with magic squares, alpha-magic squares, and geo-magic squares.)
Only the fool would take trouble to verify that his sentence was composed of ten a’s, three b’s, four c’s, four d’s, forty-six e’s, sixteen f’s, four g’s, thirteen h’s, fifteen i’s, two k’s, nine l’s, four m’s, twenty-five n’s, twenty-four o’s, five p’s, sixteen r’s, forty-one s’s, thirty-seven t’s, ten u’s, eight v’s, eight w’s, four x’s, eleven y’s, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single!
Just as an autogram is a sentence that describes itself, so there exist closed chains of sentences each of which describes its predecessor in the chain. Viewed thus, an autogram is such a chain of length 1. Here follows a chain of length 2:
The right-hand sentence contains four a's, one b, three c's, three d's, thirty-nine e's, ten f's, one g, eight h's, eight i's, one j, one k, four l's, one m, twenty-three n's, fifteen o's, one p, one q, nine r's, twenty-three s's, twenty-one t's, four u's, seven v's, six w's, two x's, five y's, and one z.
The left-hand sentence contains four a's, one b, three c's, three d's, thirty-five e's, seven f's, four g's, eleven h's, eleven i's, one j, one k, one l, one m, twenty-six n's, fifteen o's, one p, one q, ten r's, twenty-three s's, twenty-two t's, four u's, three v's, five w's, two x's, five y's, and one z.