A101639 Positive integers n for which n = f(n), where f(n) is the total number of 2's required when writing out all numbers between 0 and n.

28263827, 35000000, 242463827, 500000000, 528263827, 535000000, 10000000000, 10028263827, 10035000000, 10242463827, 10500000000, 10528263827, 10535000000

Offset: 1

Author

Ryan Propper, Dec 10 2004

Keywords

• nonn
• base
• fini
• full

Comments

Related to a problem posed by Google and discussed on the MathWorld link.

This is the complete list of all 13 positive numbers n such that n is equal to the number of 2's in the decimal digits of all numbers <= n. - Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007

Examples

			a(1) = 28263827 since writing out all numbers from 0 to 28263827 requires that 28263827 2's be used and since 28263827 is the first such positive integer.
a(4) = 500000000 because the number of 2's in the decimal digits of the numbers from 1 to 500000000 is 500000000 and this is the 4th such number.
		

Links

• Tanya Khovanova and Gregory Marton, Archive Labeling Sequences, arXiv:2305.10357 [math.HO], 2023.
• Mathworld, Problem 17 of Google Labs Aptitude Test Partially Answered, MathWorld Headline News, October 13 2004.

Crossrefs

Cf. A014778 for proof these sequences are finite; Also A101640, A101641, A130427, A130428, A130429, A130430, A130431; cf. A130432 for the number of numbers in these sequences.

Extensions

More terms from Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007