Self-Referencing English Number #3

Computer Science Level pending

Suppose we want to convert a positive integer into a word in American English spelling, and hyphens are treated as spaces, and compute its word product , which is simply the product of lengths of each words formed.

For example,

The number 24 can be written as twenty four , its word product is $W_P(24) = 6\times 4 = 24.$
The number 1011 can be written as one thousand eleven , so $W_P(1011) = 3\times 8\times6 = 144$ .

Let $N_1, N_2, N_3,\ldots$ be an increasing sequence of numbers for which $W_P(N) = N.$ Then, $N_1 = 4$ and $N_2 = 24$ . It turns out that it is a known sequence: A058230 .

$N_9$ is a 42-digit number, find the 3 leftmost digits of this number.

See Part 1 (7 $^\text{th}$ smallest) and Part 2 (8 $^\text{th}$ smallest) here.

The answer is 887.

1 solution

Jonathan Pappas
Mar 17, 2021

$887165996513213819259682435576627200000000$ is the 9th smallest such number because:

eight hundred eighty seven duodecillion one hundred sixty five undecillion nine hundred ninety six decillion five hundred thirteen nonillion two hundred thirteen octillion eight hundred nineteen septillion two hundred fifty nine sextillion six hundred eighty two quintillion four hundred thirty five quadrillion five hundred seventy six trillion six hundred twenty seven billion two hundred million

$5*7*6*5*12*3*7*5*4*11*4*7*6*3*9*4*7*8*9*3*7*8*9*5*7*8*10*3*7*5*4*10*3*7*6*3*11*4*7*6*4*11*4*7*7*3*8*3*7*6*5*7*3*7*7$

The result of the product is: $887165996513213819259682435576627200000000$

I'm drafting an edit on OEIS here to add my 3 new terms to the sequence.

Self-Referencing English Number #3

The answer is 887.

1 solution

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