%I #15 Apr 17 2020 14:18:31

%S 47,74,77,89,98,407,449,470,494,578,587,668,686,704,707,740,758,770,

%T 785,788,809,857,866,875,878,887,890,908,944,980,1124,1139,1142,1148,

%U 1157,1175,1178,1184,1187,1193,1214,1241,1319,1367,1376,1391,1412,1418,1421

%N Numbers that eventually reach the fixed point 407 under "x -> sum of cubes of digits of x" (see A055012).

%C A165330(a(n)) = 407.

%F Complement of A165334 with respect to A016789; a(n) mod 3 = 2.

%e a(4)=89: 89 -> 8^3+9^3=1241 -> 1+2^3+4^3+1=74 -> 7^3+4^3=407.

%t f[n_] := Plus@@(IntegerDigits[n]^3); Trajectory[n_] := Most[NestWhileList[f,n,UnsameQ,All]]; Select[Range[1421], Last[Trajectory[#]]==407 &] (* _Ant King_, May 24 2013 *)

%t Select[Range[1500],FixedPoint[Total[IntegerDigits[#]^3]&,#,100]==407&] (* _Harvey P. Dale_, Apr 17 2020 *)

%Y Subsequence of A031179.

%Y Cf. A046197, A035504, A008585, A165333.

%K base,nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 17 2009