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

Author

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

Keywords

• nonn
• fini
• full
• base

Examples

			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.
		

References

• J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie 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.

Crossrefs

Cf. A072409.

Programs

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)== #&]

Formula

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