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A047696 Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes. 3
1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, 933528127886302221000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sometimes called cab-taxi (or cabtaxi) numbers.

For a(10), see the C. Boyer link.

Christian Boyer: After his recent work on Taxicab(6) confirming the number found as an upper bound by Randall Rathbun in 2002, Uwe Hollerbach (USA) confirmed this week that my upper bound constructed in Dec 2006 is really Cabtaxi(10). See his announcement. - Jonathan Vos Post, Jul 08 2008

a(11) <= 11358236731992639122907000. - PoChi Su, May 20 2013

a(12) <= 277016035656568475568578823000. - PoChi Su, May 20 2013

a(13) <= 15200423908547225391399057175656000. - PoChi Su, May 23 2013

a(14) <= 1208540103696864249193964838864881592000. - PoChi Su, May 23 2013

a(12) <= 1912223147184127402358643000. - PoChi Su, Jun 01 2013

a(13) <= 46637210336673683216124944127000. - PoChi Su, Jun 01 2013

a(14) <= 3707984682237914531464445932705389000. - PoChi Su, Jun 01 2013

a(15) <= 31136289927061691188910174934641764248000. - PoChi Su, Jun 01 2013

a(16) <= 2475553003230893881356681278528562750065736000. - PoChi Su, Jun 01 2013

REFERENCES

C. Boyer, "Les nombres Taxicabs", in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

R. K. Guy, Unsolved Problems in Number Theory, Section D1.

LINKS

Table of n, a(n) for n=1..10.

D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)

D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)

C. Boyer, New upper bounds on Taxicab and Cabtaxi numbers

Uwe Hollerbach, The tenth cabtaxi number is 933528127886302221000, May 14, 2008.

Eric Weisstein's World of Mathematics, Taxicab Numbers

Eric Weisstein's World of Mathematics, Cabtaxi Number

Wikipedia, Cabtaxi number

EXAMPLE

91 = 6^3 - 5^3 = 4^3 + 3^3 (in two ways).

Cabtaxi(9)=424910390480793000 = 645210^3 + 538680^3 = 649565^3 + 532315^3 = 752409^3 - 101409^3 = 759780^3 - 239190^3 = 773850^3 - 337680^3 = 834820^3 - 539350^3 = 1417050^3 - 1342680^3 = 3179820^3 - 3165750^3 = 5960010^3 - 5956020^3.

CROSSREFS

Cf. A011541, A047697.

Sequence in context: A020218 A217841 A084319 * A043459 A038488 A213287

Adjacent sequences:  A047693 A047694 A047695 * A047697 A047698 A047699

KEYWORD

nonn,nice,more,hard

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(9) from Duncan Moore (Duncan.Moore(AT)nnc.co.uk), Feb 01 2005. This term was found on Jan 31 2005.

STATUS

approved

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Last modified July 31 17:29 EDT 2014. Contains 245085 sequences.