A075774 Number of syllables in n in American English.

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, 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, 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

Offset: 0

Author

Ethan B. Trewhitt, Oct 09 2002

Keywords

• easy
• nonn
• word

Comments

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

From Michael S. Branicky, May 28 2024: (Start)

The only numbers with a(n) = 1 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12.

The only numbers with a(n) = 2 are 7, 13, 14, 15, 16, 18, 19, 20, 30, 40, 50, 60, 80, 90.

Those with a(n) = 3 and 4 are in A372807 and A180961, respectively. (End)

Examples

			a(76)=4 because seventy-six is split sev.en.ty.six, or four syllables.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Number

Crossrefs

Cf. A005589, A052360, A180961, A372807.

Programs

PARI

A075774(n, t=[10^9, 2, 10^6, 2, 1000, 2, 100, 2])={ n>99 && forstep( i=1, #t, 2, nA075774(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

Python

def A075774(n):
    t = [(10**i, 2) for i in [12, 9, 6, 3, 2]]
    if n > 99:
        for ti, sti in t:
            if n >= ti:
                q, r = divmod(n, ti)
                return A075774(q) + sti + (A075774(r) if r else 0)
    if n < 20:
        return 1 + (n in {0, 7, 13, 14, 15, 16, 18, 19}) + 2*(n in {11, 17})
    else: return 2 + (n//10==7) + (A075774(n%10) if n%10 else 0)
print([A075774(n) for n in range(105)]) # Michael S. Branicky, Jun 27 2021 after M. F. Hasler

Extensions

More terms from Eric W. Weisstein, May 11 2006