A101639 - OEIS

%I #22 Oct 04 2023 05:10:06

%S 28263827,35000000,242463827,500000000,528263827,535000000,

%T 10000000000,10028263827,10035000000,10242463827,10500000000,

%U 10528263827,10535000000

%N 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.

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

%C 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

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

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

%e 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.

%e 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.

%Y 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.

%K nonn,base,fini,full

%O 1,1

%A _Ryan Propper_, Dec 10 2004

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