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A003294
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Numbers k such that k^4 can be written as a sum of four positive 4th powers.
(Formerly M5446)
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18
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353, 651, 706, 1059, 1302, 1412, 1765, 1953, 2118, 2471, 2487, 2501, 2604, 2824, 2829, 3177, 3255, 3530, 3723, 3883, 3906, 3973, 4236, 4267, 4333, 4449, 4557, 4589, 4942, 4949, 4974, 5002, 5208, 5281, 5295, 5463, 5491, 5543, 5648, 5658
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OFFSET
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1,1
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COMMENTS
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Sequence gives solutions k to the Diophantine equation A^4 + B^4 + C^4 + D^4 = k^4.
A138760 (numbers k such that k^4 is a sum of 4th powers of four nonzero integers whose sum is k) is a subsequence. - Jonathan Sondow, Apr 06 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Wells, Curious and interesting numbers, Penguin Books, p. 139.
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LINKS
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EXAMPLE
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353^4 = 30^4 + 120^4 + 272^4 + 315^4.
651^4 = 240^4 + 340^4 + 430^4 + 599^4.
2487^4 = 435^4 + 710^4 + 1384^4 + 2420^4.
2501^4 = 1130^4 + 1190^4 + 1432^4 + 2365^4.
2829^4 = 850^4 + 1010^4 + 1546^4 + 2745^4.
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MATHEMATICA
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fourthPowerSums = {};
Do[a4 = a^4; Do[b4 = b^4; Do[c4 = c^4; Do[d4 = d^4; e4 = a4 + b4 + c4 + d4; e = Sqrt[Sqrt[e4]]; If[IntegerQ[e], AppendTo[fourthPowerSums, e]], {d, c + 1, 9000}], {c, b + 1, 6000}], {b, a + 1, 5000}], {a, 30, 3000}];
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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Corrected and extended by Don Reble, Jul 07 2007
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STATUS
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approved
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