0,3

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)

T. D. Noe, Table of n, a(n) for n=0..11000

A055012(n) = n iff n is in A046197 = {0, 1, 153, 370, 371, 407}. - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 18 2006

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

for n from 0 to 5 do seq(n^3+j^3, j=0..9 ); od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2006

Cf. A003132.

Cf. A046197 Fixed points for operation of repeatedly replacing a number by the sum of the cubes of its digits; 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 this_sequence A069939 A118880 A048390

Adjacent sequences: A055009 A055010 A055011 this_sequence A055013 A055014 A055015

base,nonn

Henry Bottomley (se16(AT)btinternet.com), May 31 2000