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%I #26 May 28 2024 09:39:03
%S 2,1,1,1,1,1,1,2,1,1,1,3,1,2,2,2,2,3,2,2,2,3,3,3,3,3,3,4,3,3,2,3,3,3,
%T 3,3,3,4,3,3,2,3,3,3,3,3,3,4,3,3,2,3,3,3,3,3,3,4,3,3,2,3,3,3,3,3,3,4,
%U 3,3,3,4,4,4,4,4,4,5,4,4,2,3,3,3,3,3,3,4,3,3,2,3,3,3,3,3,3,4,3,3,3,4,4,4,4
%N Number of syllables in n in American English.
%C Uses the convention of omitting a trailing 'and', so 101 is 'one hundred one' rather than 'one hundred and one.' - _Eric W. Weisstein_, May 11 2006
%C From _Michael S. Branicky_, May 28 2024: (Start)
%C The only numbers with a(n) = 1 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12.
%C The only numbers with a(n) = 2 are 7, 13, 14, 15, 16, 18, 19, 20, 30, 40, 50, 60, 80, 90.
%C Those with a(n) = 3 and 4 are in A372807 and A180961, respectively. (End)
%H Charles R Greathouse IV, <a href="/A075774/b075774.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Number.html">Number</a>
%e a(76)=4 because seventy-six is split sev.en.ty.six, or four syllables.
%o (PARI) A075774(n, t=[10^9, 2, 10^6, 2, 1000, 2, 100, 2])={ n>99 && forstep( i=1, #t, 2, n<t[i] && next; n=divrem(n, t[i]); return( A075774(n[1])+t[i+1]+if( n[2], A075774( n[2] )))); if( n<20, 1+!!setsearch(Set([0,7,13,14,15,16,18,19]),n) + 2*!!setsearch(Set([11,17]),n), 2+(n\10==7) + if(n%10, A075774(n%10)))} \\ The "Set()" is not required in PARI v.2.6+ but we put it for downward compatibility. - _M. F. Hasler_, Nov 03 2013
%o (Python)
%o def A075774(n):
%o t = [(10**i, 2) for i in [12, 9, 6, 3, 2]]
%o if n > 99:
%o for ti, sti in t:
%o if n >= ti:
%o q, r = divmod(n, ti)
%o return A075774(q) + sti + (A075774(r) if r else 0)
%o if n < 20:
%o return 1 + (n in {0, 7, 13, 14, 15, 16, 18, 19}) + 2*(n in {11, 17})
%o else: return 2 + (n//10==7) + (A075774(n%10) if n%10 else 0)
%o print([A075774(n) for n in range(105)]) # _Michael S. Branicky_, Jun 27 2021 after _M. F. Hasler_
%Y Cf. A005589, A052360, A180961, A372807.
%K easy,nonn,word
%O 0,1
%A Ethan B. Trewhitt, Oct 09 2002
%E More terms from _Eric W. Weisstein_, May 11 2006
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