[seqfan] Re: New sequence?

[Hans Havermann]

NJAS: "That sequence seems a bit too artificial for the OEIS. Anything that depends on the English words for the numbers already has a count against it, and the fact that there is no canonical version also makes it of less interest."

Notwithstanding, Claudio's proposed sequence has an interesting history. In 1981, A. Ross Eckler wrote an article in Word Ways called "Alphabetizing the Integers" (Vol. 14, #1, pages 18-20):

https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=2556&context=wordways

Eckler quotes Howard Bergerson: "I have had one research problem in mind for a long time -- I once did some preliminary work on it -- which could turn out to be any­thing from easy to formidable to practically impossible. It is this: Imagine the one thousand vigintillion minus one (if you don't in­clude zero) consecutively named numbers arranged in alphabetical order and also in numerical order. How many (if any) numbers have their positions the same in both lists? What is the least such number? ... Does this intrigue you enough to have a shot at it?"

Eckler has a shot at it, noting on page 20 that "Philip Cohen has pointed out that Bergerson's problem can be re­garded as one member of a class of matching problems: the integers 1 through n can be alphabetized, where n takes on any integral value." This is followed by nine lists of small-integer names with underlines corresponding to Claudio's [[1], [1, 2], [1], [3], 0, 0, 0, [6], 0, ...].

Mathematica has progressed from its once-largest IntegerName[10^66-1] to IntegerName[10^306-1] so, while perhaps not yet canonical, the problem could be restated using the much larger number range.

Eckler notes an alphabetization-interpretation issue at the end but clearly states a preference for his article that "the space is assumed to precede the letter A in alphabetization (e.g., eight hundred before eighteen)."