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.

1, 136, 153, 244, 370, 371, 407, 919, 1459

Offset

1,2

References

J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 257 pp. 41; 185 Ellipses Paris 2004.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, London, England, 1997, pp. 124-125.

Links

Table of n, a(n) for n=1..9.

Formula

n such that f(f(n)) = n, where f(k) = A055012(k). - Lekraj Beedassy, Sep 10 2004

Example

136 is included because 1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.
244 is included because 2^3 + 4^3 + 4^3 = 136 and 1^3 + 3^6 + 6^3 = 244.

Mathematica

f[n_] := Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[n]^3]]^3]; Select[ Range[10^7], f[ # ] == # &]
Select[Range[10000], Plus@@IntegerDigits[Plus@@IntegerDigits[ # ]^3]^3)== #&]

Crossrefs

Cf. A072409.

Sequence in context: A269062 A270301 A281241 * A072889 A157714 A165337

Adjacent sequences: A072881 A072882 A072883 * A072885 A072886 A072887

Keyword

nonn,fini,full,base

Author

Robert G. Wilson v and Harvey P. Dale, Aug 09 2002

Status

approved