A359534 Numbers that don’t have a 1 and yet have one.

2000008, 2000080, 2000082, 2000083, 2000084, 2000085, 2000086, 2000087, 2000088, 2000089, 2000800, 2000802, 2000803, 2000804, 2000805, 2000806, 2000807, 2000808, 2000809, 2000820, 2000822, 2000823, 2000824, 2000825, 2000826, 2000827, 2000828, 2000829, 2000830, 2000832, 2000833, 2000834, 2000835, 2000836, 2000837, 2000838

Offset: 1

Author

Eric Angelini, Oct 15 2023

Keywords

• base
• nonn
• word

Examples

			The first three terms are 2000008, 2000080 and 2000082 where no digit 1 is present, and yet we can read the substring ONE when those numbers are written in English: two milli(ON E)ight, two milli(ON E)ighty, two milli(ON E)ighty two, etc.
We cannot use Eleven after milliON, nor Eighteen, as this would produce at least one digit 1.
		

Crossrefs

Cf. A052383, A345711.

Programs

Mathematica

Select[Range[#, # + 1000] &[2*10^6], And[StringContainsQ[StringJoin@ DeleteCases[Characters@ IntegerName[#, "Words"], ?(! LetterQ[#] &)], "one"], DigitCount[#, 10, 1] == 0] &] (* _Michael De Vlieger, Oct 15 2023 *)

Python

from num2words import num2words
def n2w(n): return num2words(n).replace(" and","").replace(chr(44),"").replace("-","").replace(" ","")
def ok(n): return "1" not in str(n) and "one" in n2w(n)
print([k for k in range(2000840) if ok(k)]) # Michael S. Branicky, Oct 15 2023