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%I #14 Jul 25 2017 02:18:52
%S 1,136,153,244,370,371,407,919,1459
%N 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.
%D J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 257 pp. 41; 185 Ellipses Paris 2004.
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, London, England, 1997, pp. 124-125.
%F n such that f(f(n)) = n, where f(k) = A055012(k). - _Lekraj Beedassy_, Sep 10 2004
%e 136 is included because 1^3 + 3^3 + 6^3 = 244 and 2^3 + 4^3 + 4^3 = 136.
%e 244 is included because 2^3 + 4^3 + 4^3 = 136 and 1^3 + 3^6 + 6^3 = 244.
%t f[n_] := Apply[Plus, IntegerDigits[Apply[Plus, IntegerDigits[n]^3]]^3]; Select[ Range[10^7], f[ # ] == # &]
%t Select[Range[10000], Plus@@IntegerDigits[Plus@@IntegerDigits[ # ]^3]^3)== #&]
%Y Cf. A072409.
%K nonn,fini,full,base
%O 1,2
%A _Robert G. Wilson v_ and _Harvey P. Dale_, Aug 09 2002
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