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Search: id:A050801
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| A050801 |
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Numbers n such that n^2 is expressible as the sum of two nonzero cubes in at least one way. |
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+0
4
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| 3, 4, 24, 32, 81, 98, 108, 168, 192, 228, 256, 312, 375, 500, 525, 588, 648, 671, 784, 847, 864, 1014, 1029, 1183, 1225, 1261, 1323, 1344, 1372, 1536, 1824, 2048, 2187, 2496, 2646, 2888, 2916, 3000, 3993, 4000, 4200, 4225, 4536, 4563, 4644, 4704, 5184, 5324
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Analogous solutions exist for the sum of two identical cubes z^2 = 2*r^3 (e.g. 864^2 = 2*72^3). Values of 'z' are the terms in A033430, values of 'r' are the terms in A001105.
First term that can be expressed in two ways: 77976 = 228^3+1824^3 = 1026^3+1710^3 - Jud McCranie (j.mccranie(AT)comcast.net).
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REFERENCES
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Ian Stewart, "Game, Set and Math", Chapter 8, 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
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LINKS
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T. D. Noe and Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
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E.g. 1183^2 = 65^3 + 104^3.
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PROGRAM
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(PARI) { nstart=1; astart=3; n=nstart; a=astart-1; until (0, a=a+1; a2=a*a; b1=((a2/2)^(1/3))\1; for (b=b1, a, b3=b*b*b; c1=1; if (a2 > b3, c1=((a2-b3)^(1/3))\1; ); for (c=c1, b, d=b3 + c*c*c; if (d > a2 && c == 1, break(2)); if (d > a2, break); if (a2 == d, print(n, " ", a); write("b050801.txt", n, " ", a); n=n+1; break(2); ); ) ) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jan 15 2009]
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CROSSREFS
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Cf. A050802, A000404, A033430, A001105.
Sequence in context: A032831 A047180 A051394 this_sequence A103093 A124632 A048091
Adjacent sequences: A050798 A050799 A050800 this_sequence A050802 A050803 A050804
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KEYWORD
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nonn,nice
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Sep 15 1999.
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) and Jud McCranie (j.mccranie(AT)comcast.net).
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