A101641 - OEIS

%I #25 Feb 16 2025 08:32:55

%S 499999984,499999985,499999986,499999987,499999988,499999989,

%T 499999990,499999991,499999992,499999993,500000000,10000000000,

%U 10499999984,10499999985,10499999986,10499999987,10499999988,10499999989

%N 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.

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

%C 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

%H Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007, <a href="/A101641/b101641.txt">Table of n, a(n) for n = 1..47</a>

%H Tanya Khovanova and Gregory Marton, <a href="https://arxiv.org/abs/2305.10357">Archive Labeling Sequences</a>, arXiv:2305.10357 [math.HO], 2023. See p. 4.

%H Mathworld, <a href="https://mathworld.wolfram.com/news/2004-10-13/google/">Problem 17 of Google Labs Aptitude Test Partially Answered</a>, MathWorld Headline News, October 13 2004.

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

%e 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.

%e 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.

%Y 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.

%K nonn,base,fini,full,changed

%O 1,1

%A _Ryan Propper_, Dec 11 2004

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

%E Keyword added by _Charles R Greathouse IV_, Jul 22 2010