A371510 Number of swaps needed to bubble-sort the US English name of n.
4, 3, 2, 8, 1, 3, 1, 5, 2, 4, 2, 4, 9, 16, 16, 10, 13, 17, 11, 13, 5, 21, 14, 34, 21, 25, 16, 30, 29, 27, 3, 20, 11, 32, 18, 23, 12, 28, 27, 25, 0, 15, 7, 25, 11, 17, 8, 22, 20, 21, 1, 13, 7, 25, 10, 15, 7, 21, 17, 16, 2, 18, 12, 31, 18, 21, 11, 26, 25, 23, 6, 22, 15, 35, 22, 25, 16, 29, 30, 28, 2, 14, 8, 26, 13, 18, 8, 22, 19, 17, 4, 16, 10, 30, 15, 22, 12, 24, 26, 21, 28
Offset: 0
Examples
For n=0, "zero" requires a(0) = 4 swaps of adjacent letters to reach ascending alphabetical order: ZERO-->EZRO-EZOR-EOZR-EORZ.
Links
- Eric Angelini and Nicolas Graner, More bubble sorting, personal blog, March 2024.
- Hans Havermann, Graph of terms to one million
Crossrefs
Cf. A371478 (fixed points).
Programs
-
Python
from num2words import num2words def a(n): s = [c for c in num2words(n).replace(" and", "") if c.isalpha()] L, c, swap = list(s), 0, True while swap: swap = False for i in range(len(L)-1): if L[i] > L[i+1]: L[i], L[i+1], c, swap = L[i+1], L[i], c+1, True return c print([a(n) for n in range(101)]) # Michael S. Branicky, Mar 25 2024
Comments