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A174979
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Smallest prime p which is a concatenation of n^3 and the cubic digits 0, 1, 8.
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1
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11, 181, 127, 641, 11251, 2161, 10343, 15121, 10729, 1000081, 81331, 117281, 12197, 1274401, 33751, 40961, 84913, 58321, 106859, 180001, 89261, 1064801, 812167, 138241, 8156251, 10175761, 196831, 2195201, 2438911, 270001, 297911
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OFFSET
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1,1
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COMMENTS
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There are three decimal digits which are cubes: 0 = 0^3, 1 = 1^3, 8 = 2^3. It is conjectured that sequence is infinite.
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REFERENCES
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J.-P. Allouche, J. Shallit: Automatic Sequences, Theory, Applications, Generalizations, Cambridge University Press, 2003
C. Dumitrescu and V. Seleacu: Some Notions and Questions in Number Theory, Glendale, Arizona, Erhus University Press, 1994
O. Oystein: Number Theory and its History, Dover Classics of Science and Mathematics, 1988
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LINKS
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EXAMPLE
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41^3 = 68921, and 1689211 is the smallest prime which can be produced by concatenating 68921 with some combination of the digits 0, 1, and 8.
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 03 2010
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EXTENSIONS
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STATUS
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approved
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