A132363 Least natural number in English which requires exactly n characters to spell including spaces and hyphens, or 0 if no such number exists. The inverse of A052360.

1, 0, 3, 11, 15, 13, 17, 21, 24, 23, 73, 3000, 101, 104, 103, 111, 115, 113, 117, 121, 124, 123, 173, 323, 373, 1101, 1104, 1103, 1111, 1115, 1113, 1117, 1121, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 21373, 23323, 23373, 73373

Offset: 3

Author

Jonathan Vos Post, Nov 08 2007

Keywords

• easy
• nonn
• word

Comments

This is to A052360 as A134629 is to A005589. Also assumes no 'and' is used to spell integers. This deviates from A134629 at a(10). "twenty-one" is the smallest integer whose standard English name has a hyphen. "one hundred" is the smallest integer whose standard English name has a space. "one hundred twenty-one" is the smallest integer whose standard English name has a space and a hyphen.

Examples

			a(3) = 1 because "one" has 3 characters.
a(4) = 0 because "zero" has 4 characters.
a(5) = 3 because "three" has 5 characters.
a(6) = 11 because "eleven" has 6 characters.
a(7) = 15 because "fifteen" has 7 characters.
a(8) = 13 because "thirteen" has 8 characters.
a(9) = 17 because "seventeen" has 9 characters.
a(10) = 21 because "twenty-one" has 10 characters.
a(11) = 24 because "twenty-four" has 11 characters.
a(12) = 23 because "twenty-three" has 12 characters.
a(13) = 73 because "seventy-three" has 13 characters.
a(14) = 3000 because "three thousand" has 14 characters.
		

Links

• Eric Weisstein's World of Mathematics, Number

Crossrefs

Cf. A005589, A052360, A119960, A129774, A134629.

Extensions

Corrected and extended by Martin Fuller, Nov 24 2007