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A371510 Number of swaps needed to bubble-sort the US English name of n.

%I A371510 #17 Mar 26 2024 13:19:06
%S A371510 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,
%T A371510 30,29,27,3,20,11,32,18,23,12,28,27,25,0,15,7,25,11,17,8,22,20,21,1,
%U A371510 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
%N A371510 Number of swaps needed to bubble-sort the US English name of n.
%C A371510 No swaps involve hyphens or spaces.
%H A371510 Eric Angelini and Nicolas Graner, <a href="https://cinquantesignes.blogspot.com/2024/03/more-bubble-sorting.html">More bubble sorting</a>, personal blog, March 2024.
%H A371510 Hans Havermann, <a href="/A371510/a371510.png">Graph of terms to one million</a>
%e A371510 For n=0, "zero" requires a(0) = 4 swaps of adjacent letters to reach ascending alphabetical order: ZERO-->EZRO-EZOR-EOZR-EORZ.
%o A371510 (Python)
%o A371510 from num2words import num2words
%o A371510 def a(n):
%o A371510     s = [c for c in num2words(n).replace(" and", "") if c.isalpha()]
%o A371510     L, c, swap = list(s), 0, True
%o A371510     while swap:
%o A371510         swap = False
%o A371510         for i in range(len(L)-1):
%o A371510             if L[i] > L[i+1]:
%o A371510                 L[i], L[i+1], c, swap = L[i+1], L[i], c+1, True
%o A371510     return c
%o A371510 print([a(n) for n in range(101)]) # _Michael S. Branicky_, Mar 25 2024
%Y A371510 Cf. A371478 (fixed points).
%K A371510 base,nonn,word
%O A371510 0,1
%A A371510 _Eric Angelini_ and Nicolas Graner, Mar 25 2024