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A154820 Numbers whose trajectory under iteration of sum of cubes of digits eventually turns out to follow the cyclic iteration of 133, 55, 250.

%I A154820 #14 Jan 07 2019 04:20:21
%S A154820 4,13,25,28,31,40,46,52,55,64,82,103,130,133,205,208,250,256,265,280,
%T A154820 289,298,301,310,313,331,349,394,400,406,439,448,460,484,493,502,505,
%U A154820 520,526,550,562,589,598,604,625,640,652,679,697,769,796,802,820,829
%N A154820 Numbers whose trajectory under iteration of sum of cubes of digits eventually turns out to follow the cyclic iteration of 133, 55, 250.
%C A154820 All the numbers are of the form 3n+1.
%C A154820 Subsequence of A165336. - _Reinhard Zumkeller_, Sep 17 2009
%e A154820 Taking 40 for example,
%e A154820   4^3 + 0^3 = 64;
%e A154820   6^3 + 4^3 = 280;
%e A154820   2^3 + 8^3 + 0^3 = 520;
%e A154820   5^3 + 2^3 + 0^3 = 133;
%e A154820   1^3 + 3^3 + 3^3 = 55;
%e A154820   5^3 + 5^3 = 250.
%p A154820 A055012 := proc(n) local a,d ; a := 0 ; for d in convert(n,base,10) do a := a+d^3; od; a ; end: isA154820 := proc(n) local traj,t ; t := n ; traj := {} ; while true do if t in traj then if t in {133,55,250} then RETURN(true) ; else RETURN(false) ; fi; else traj := traj union {t} ; t := A055012(t) ; fi; od: end: for n from 1 to 1000 do if isA154820(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Jan 18 2009
%Y A154820 Cf. A165337, A154877, A165336, A165339.
%K A154820 nonn,base
%O A154820 1,1
%A A154820 Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 15 2009
%E A154820 Extended by _R. J. Mathar_, Jan 18 2009
%E A154820 Edited by _Charles R Greathouse IV_, Aug 02 2010