cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A101639 #23 Feb 16 2025 08:32:55
%S A101639 28263827,35000000,242463827,500000000,528263827,535000000,
%T A101639 10000000000,10028263827,10035000000,10242463827,10500000000,
%U A101639 10528263827,10535000000
%N 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.
%C A101639 Related to a problem posed by Google and discussed on the MathWorld link.
%C A101639 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 A101639 Tanya Khovanova and Gregory Marton, <a href="https://arxiv.org/abs/2305.10357">Archive Labeling Sequences</a>, arXiv:2305.10357 [math.HO], 2023.
%H A101639 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.
%e A101639 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 A101639 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 A101639 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 A101639 nonn,base,fini,full
%O A101639 1,1
%A A101639 _Ryan Propper_, Dec 10 2004
%E A101639 More terms from Daniel Hirschberg (dan(AT)ics.uci.edu), May 05 2007