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

0,1

Comments

No swaps involve hyphens or spaces.

Links

Table of n, a(n) for n=0..100.

Eric Angelini and Nicolas Graner, More bubble sorting, personal blog, March 2024.

Hans Havermann, Graph of terms to one million

Example

For n=0, "zero" requires a(0) = 4 swaps of adjacent letters to reach ascending alphabetical order: ZERO-->EZRO-EZOR-EOZR-EORZ.

Prog

(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

Crossrefs

Cf. A371478 (fixed points).

Sequence in context: A307648 A067016 A022295 * A258415 A132668 A018866

Adjacent sequences: A371507 A371508 A371509 * A371511 A371512 A371513

Keyword

base,nonn,word

Author

Eric Angelini and Nicolas Graner, Mar 25 2024

Status

approved