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%I #9 Jul 25 2017 02:18:40
%S 1,4150,4151,54748,58618,76438,89883,92727,93084,157596,194979
%N 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.
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, London, England, 1997, pp. 157, 168.
%e 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.
%t f[n_] := Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[n]^5]]^5]; Select[ Range[10^7], f[ # ] == # &]
%t di5Q[n_]:=Module[{k=Total[IntegerDigits[n]^5]},Total[ IntegerDigits[k]^5] == n]; Select[Range[200000],di5Q] (* _Harvey P. Dale_, Nov 26 2014 *)
%Y Cf. A072409.
%K nonn,fini,full,base
%O 1,2
%A _Robert G. Wilson v_, Aug 09 2002
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