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A055012
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Sum of cubes of digits of n.
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32
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0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1, 2, 9, 28, 65, 126, 217, 344, 513, 730, 8, 9, 16, 35, 72, 133, 224, 351, 520, 737, 27, 28, 35, 54, 91, 152, 243, 370, 539, 756, 64, 65, 72, 91, 128, 189, 280, 407, 576, 793, 125, 126, 133, 152, 189, 250, 341, 468, 637, 854
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n > 1999, a(n) < n. The iteration of this map on n either stops at a fixed point (A046197) or has a period of length 2 or 3: {55,250,133}, {136,244}, {160,217,352}, or {919,1459}. - T. D. Noe, Jul 17 2007
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009: (Start)
a(n) <= 729*A055642(n);
a(A165370(n)) = n and a(m) <> n for m < A165370(n);
A165330 and A165331 give the final value and the number of steps when iterating until a fixed point or cycle is reached;
a(A165332(n)) = A165332(n);
a(a(A165336(n)))=A165336(n) or a(a(a(A165336(n))))=A165336(n). (End)
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..11000
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FORMULA
| a(n)=sum{k>0, (floor(n/10^k)-10*floor(n/10^(k+1)))^3}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 25 2007
a(10n+k)=a(n)+k^3, 0<=k<10. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 25 2007
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MAPLE
| A055012 := proc(n)
add(d^3, d=convert(n, base, 10)) ;
end proc: # R. J. Mathar, Dec 15 2011
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MATHEMATICA
| Total/@((IntegerDigits/@Range[0, 60])^3) (* From Harvey P. Dale, Jan 27 2012 *)
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CROSSREFS
| Cf. A003132.
Cf. A046197 Fixed points; A046459 The only integers equal to the sum of the digits of their cubes; A072884 3rd order digital invariants: the sum of the cubes of the digits of n equals some number k and the sum of the cubes of the digits of k equals n; A061212 cubes with the property that the sum of the cubes of the digits is also a cube.
Cf. A003132.
Cf. A007953, A055017, A076313, A076314.
A165340. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009]
Sequence in context: A017670 A126200 A076989 * A069939 A118880 A048390
Adjacent sequences: A055009 A055010 A055011 * A055013 A055014 A055015
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 31 2000
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