Search: id:A014778
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%I A014778
%S A014778 0,1,199981,199982,199983,199984,199985,199986,199987,199988,199989,
%T A014778 199990,200000,200001,1599981,1599982,1599983,1599984,1599985,1599986,
%U A014778 1599987,1599988,1599989,1599990,2600000,2600001,13199998,35000000
%N A014778 List of numbers n such that n is equal to the number of 1's in the decimal 
               digits of all numbers <= n.
%C A014778 The full list of 84 terms is given in the b-file.
%C A014778 It can be proved that this sequence is finite. (The main idea of the 
               proof is that the number of 1's used in positive integers <= n is 
               greater than or equal to A(n) = (1/10) number of digits in positive 
               integers from 1 to n = (1/10) Sum_{i=1,...n} (1+Floor(log_10 i)). 
               By considering the area below a logarithmic function and the corresponding 
               integral, it can be shown that A(n)/n goes to infinity.) - Joseph 
               L. Pe (joseph_l_pe(AT)hotmail.com), Nov 05 2002
%C A014778 Fixed points of A094798. Sequence consists of six runs of ten consecutive 
               numbers, ten pairs of consecutive numbers and four isolated numbers. 
               - David Wasserman (dwasserm(AT)earthlink.net), Jun 29 2007
%D A014778 Maurice Protat "Des Olympiades a` l'Agr'egation", Editions Ellipses, 
               Paris 1997, p. 183.
%H A014778 Graeme McRae (g_m(AT)mcraefamily.com), May 26 2007, <a href="b014778.txt">
               Table of n, a(n) for n = 1..84</a>
%H A014778 Pegg, E. Jr. and Weisstein, E. W. <a href="http://mathworld.wolfram.com/
               news/2004-10-13/google/">Mathematica's Google Aptitude.</a> MathWorld 
               Headline news, Oct 13, 2004.
%e A014778 a(5)=199983 because the number of 1's in the decimal digits of the numbers 
               from 0 to 199983 is 199983 and this is the 5th such number.
%Y A014778 Cf. A101639, A101640, A101641, A130427, A130428, A130429, A130430, A130431; 
               Cf. A130432 for the number of numbers in these sequences.
%Y A014778 Cf. A094798.
%Y A014778 Sequence in context: A099818 A043592 A126558 this_sequence A094799 A163500 
               A164321
%Y A014778 Adjacent sequences: A014775 A014776 A014777 this_sequence A014779 A014780 
               A014781
%K A014778 base,fini,nonn,full
%O A014778 1,3
%A A014778 Yves Babe, Maurice Protat, Olivier Gerard (olivier.gerard(AT)gmail.com)
%E A014778 Corrected and extended by Deepan Majmudar (deepan.majmudar(AT)hp.com), 
               Nov 19 2004
%E A014778 41 further terms from Ryan Propper (rpropper(AT)stanford.edu), Dec 07 
               2004, who observed that there are no more terms <= 10^9.
%E A014778 The final (84-th) term 1111111110 was sent by Lambrecht Kok (L.P.Kok(at)rug.nl), 
               Jan 13, 2005. He says: "H. van Haeringen and I showed that this list 
               of 84 terms is complete on Dec 15 2004".
%E A014778 Independently shown to be complete by Ryan Propper and Vaughan Pratt, 
               Jan 08 2005

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