Search: id:A011541
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%I A011541
%S A011541 2,1729,87539319,6963472309248,48988659276962496,
%T A011541 24153319581254312065344
%N A011541 Taxi-cab (taxicab) or Hardy-Ramanujan numbers: the smallest number that 
               is the sum of 2 cubes in n ways (an infinite sequence).
%D A011541 C. Boyer, "Les nombres Taxicabs", in Dossier Pour La Science, pp. 26-28, 
               Volume 59 (Jeux math') April/June 2008 Paris.
%D A011541 C. S. Calude, E. Calude and M. J. Dinneen, What is the value of Taxicab(6)?, 
               J. Universal Computer Science, 9 (2003), 1196-1203.
%D A011541 R. K. Guy, Unsolved Problems in Number Theory, D1.
%D A011541 J. Silverman, Taxicabs and Sums of Two Cubes, American Mathematical Monthly, 
               Volume 100, Issue 4 (Apr., 1993), 331-340.
%D A011541 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. 
               Penguin Books, NY, 1986, 165 and 189.
%H A011541 Anonymous, <a href="http://everything2.net/index.pl?node_id=1028223&displaytype=printable&lastnode_id=1028223\
               ">taxicab numbers</a>
%H A011541 D. J. Bernstein, <a href="http://pobox.com/~djb/papers/sortedsums.dvi">
               Enumerating solutions to p(a) + q(b) = r(c) + s(d)</a>
%H A011541 D. Bill, <a href="http://www.durangobill.com/Ramanujan.html">Durango 
               Bill's Ramanujan Numbers and The Taxicab Problem</a>
%H A011541 C. Boyer, <a href="http://www.christianboyer.com/taxicab">New upper bounds 
               on Taxicab and Cabtaxi numbers</a>
%H A011541 C. S. & E. Calude and M. T. Dinneen, <a href="http://web.archive.org/
               web/20040121183032/http://www.jucs.org/jucs_9_10/what_is_the_value/
               paper.html">What is the value of Taxicab(6)?</a>
%H A011541 U. Hollerbach, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0803&L=nmbrthry&T=0&P=1059">
               The sixth taxicab number is 24153319581254312065344</a>, posting 
               to the NMBRTHRY mailing list, Mar 09 2008
%H A011541 J. C. Meyrignac, <a href="http://euler.free.fr/taxicab.htm">The Taxicab 
               Problem</a>
%H A011541 Number Theory Archive, <a href="http://Listserv.nodak.edu/scripts/wa.exe?A2=ind0207&L=nmbrthry&F=&S=&P=1278">
               Sixth Taxicab Number?</a>
%H A011541 I. Peterson, Math Trek, <a href="http://www.sciencenews.org/20020727/
               mathtrek.asp">Taxicab Numbers</a>
%H A011541 I. Peterson, Math Trek, <a href="http://www.maa.org/mathland/mathtrek_07_22_02.html">
               Taxicab Numbers</a>
%H A011541 Randall L. Rathbun, <a href="http://listserv.nodak.edu/scripts/wa.exe?A2=ind0207&L=nmbrthry&P=R530">
               Posting to Number Theory List</a>
%H A011541 W. Schneider, <a href="http://www.wschnei.de/number-theory/taxicab-numbers.html">
               Taxicab Numbers</a>
%H A011541 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CubicNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A011541 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TaxicabNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A011541 Wikipedia, <a href="http://en.wikipedia.org/wiki/Taxicab_number">Taxicab 
               number</a>
%H A011541 D. W. Wilson, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Fifth Taxicab Number is 48988659276962496</a>, J. Integer Sequences, 
               Vol. 2, 1999, #99.1.9.
%H A011541 D. W. Wilson, <a href="http://pi.lacim.uqam.ca/eng/problem_en.html">Taxicab 
               Numbers</a>
%Y A011541 Cf. A023050, A003826, A001235, A047696.
%Y A011541 Sequence in context: A002490 A160224 A129061 this_sequence A080642 A108331 
               A162554
%Y A011541 Adjacent sequences: A011538 A011539 A011540 this_sequence A011542 A011543 
               A011544
%K A011541 nonn,nice,hard
%O A011541 1,1
%A A011541 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A011541 David W. Wilson (davidwwilson(AT)comcast.net) reports a(6) <= 8230545258248091551205888. 
               [But see next line! ]
%E A011541 Randall L. Rathbun has shown that a(6) <= 24153319581254312065344.
%E A011541 C. S. Calude, E. Calude and M. J. Dinneen, What is the value of Taxicab(6)?, 
               2003, show that with high probability, a(6) = 24153319581254312065344.
%E A011541 a(6), confirmed by Uwe Hollerbach, communicated by Schneelocke [Christian 
               Schroeder] (sloane-sequences(AT)gl00on.net), Mar 09 2008

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