A129774 Main diagonal of table of length of English names of numbers.
1, 5, 8, 30, 0, 42, 36, 47, 79, 3000000, 606, 502, 301, 305, 420, 218, 181, 176, 233, 367, 578, 2101, 2105, 1607, 1540, 1616, 1311, 1232, 1235, 1298, 1423, 1787, 3348, 3793, 11375, 13358, 13823, 17577, 23339, 23833, 37777, 101398, 103384, 103875, 111478, 113394
Offset: 1
Examples
a(1) = 1 because "one" is the first positive integer with 3 letters in its name.
a(2) = 5 because "five" is the second positive integer with 4 letters.
a(3) = 8 because "eight" is the third positive integer with 5 letters.
a(4) = 30 because "thirty" is the fourth positive integer with 6 letters.
a(5) = 0 because there are only three 7-letter positive integers: {15, 16, 70}.
Programs
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Python
def A129774(n): i, found, limit = 0, 0, 10**2 while found < n-2 and i < limit: i += 1 found += 1*(A005589(i)==n) return i*(i < limit) print([A129774(i) for i in range(3,12)]) # Michael S. Branicky, Jul 13 2020
Formula
a(n) = A(n+2,n) where A(k,n) = n-th positive integer requiring exactly k letters (not including "and" or hyphens) in its English name, or 0 if no such integer.
Extensions
Corrected and edited by Danny Rorabaugh, May 13 2016
Corrected terms a(10)-a(18) and table in comments from 9; added terms from a(20) - Michael S. Branicky, Jul 13 2020
Comments