"Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,' adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, `it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways." I've long thought that the fourth root of 9.1 was a dull number, despite a strange continued fraction. Of all the potentially dull numbers in the world, I had to chose that one. Richard Sabey wrote to me.
You say [I paraphrase, for lack of a root-symbol] "I considered 9.1^(1/4) weird, but nothing particularly special". You are too modest, this being an alternative presentation of the largest 2 consecutive 19-smooth numbers, 11859210 and 11859211, which you published in Mathpuzzle on the 23rd of December.
I didn't see the connection at all, so I asked Richard to explain. (http://www.research.att.com/projects/OEIS?Anum=A002072 , by the way, is largest consecutive n-smooth numbers)) Richard wrote: As you reported, the largest 2 consecutive 19-smooth numbers are: 11859210 ~~ 11859211 => 7*13*19^4 ~~ 2*3^4*5*11^4 => 91*19^4 ~~ 10*33^4 => 9.1 ~~ 33^4/19^4 => 9.1^(1/4) ~~ 33/19 Now I get it. So 9.1^(1/4) turns out to be interesting after all. Ed Pegg Jr