A101641 Positive integers n for which n = f(n), where f(n) is the total number of 4's required when writing out all numbers between 0 and n.

499999984, 499999985, 499999986, 499999987, 499999988, 499999989, 499999990, 499999991, 499999992, 499999993, 500000000, 10000000000, 10499999984, 10499999985, 10499999986, 10499999987, 10499999988, 10499999989

Offset: 1

Author

Ryan Propper, Dec 11 2004

Keywords

• nonn
• base
• fini
• full

Comments

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

Together with the b-file, this gives the complete list of all 47 positive numbers n such that n is equal to the number of 4's in the decimal digits of all numbers <= n. - Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007

Examples

			a(1) = 499999984, since writing out all numbers from 0 to 499999984 requires that 499999984 4's be used and since 499999984 is the first such positive integer.
a(4) = 499999987 because the number of 4's in the decimal digits of the numbers from 1 to 499999987 is 499999987 and this is the 4th such number.
		

Links

• Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007, Table of n, a(n) for n = 1..47
• Tanya Khovanova and Gregory Marton, Archive Labeling Sequences, arXiv:2305.10357 [math.HO], 2023. See p. 4.
• 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 A101639, A101640, A130427, A130428, A130429, A130430, A130431; cf. A130432 for the number of numbers in these sequences.

Formula

a(n) = 499999983 + n, n <= 10; a(n) = 500000000, n = 11

Extensions

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

Keyword added by Charles R Greathouse IV, Jul 22 2010