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A046197
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Fixed points for operation of repeatedly replacing a number with the sum of the cubes of its digits.
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26
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OFFSET
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1,3
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COMMENTS
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Suppose n has d digits; then the sum of the cubes of its digits is <= 729d and n >= 10^(d-1). So d <= 5. It is now easy to check that the numbers shown are the only solutions. [Corrected by M. F. Hasler, Apr 12 2015]
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 153, p. 50, Ellipses, Paris 2008.
G. H. Hardy, A Mathematician's Apology, Cambridge, 1967.
J. Shallit, Number theory and formal languages, in Emerging applications of number theory (Minneapolis, MN, 1996), 547-570, IMA Vol. Math. Appl., 109, Springer, New York, 1999.
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LINKS
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FORMULA
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EXAMPLE
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1^3 + 5^3 + 3^3 = 153. 3^3+7^3 +0^3 = 370.
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PROG
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CROSSREFS
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KEYWORD
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nonn,fini,full,base
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AUTHOR
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Richard C. Schroeppel
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STATUS
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approved
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