A072896 5th-order digital invariants: the sum of the 5th powers of the digits of n equals some number k and the sum of the 5th powers of the digits of k equals n.

1, 4150, 4151, 54748, 58618, 76438, 89883, 92727, 93084, 157596, 194979

Offset: 1

Author

Robert G. Wilson v, Aug 09 2002

Keywords

• nonn
• fini
• full
• base

Examples

			58618 is included because 5^5 + 8^5 + 6^5 + 1^5 + 8^5 = 76438 and 7^5 + 6^5 + 4^5 + 3^5 + 8^5 = 58618.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, London, England, 1997, pp. 157, 168.

Crossrefs

Cf. A072409.

Programs

Mathematica

f[n_] := Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[n]^5]]^5]; Select[ Range[10^7], f[ # ] == # &]
di5Q[n_]:=Module[{k=Total[IntegerDigits[n]^5]},Total[ IntegerDigits[k]^5] == n]; Select[Range[200000],di5Q] (* Harvey P. Dale, Nov 26 2014 *)