A165335 Numbers that eventually reach the fixed point 407 under "x -> sum of cubes of digits of x" (see A055012).

47, 74, 77, 89, 98, 407, 449, 470, 494, 578, 587, 668, 686, 704, 707, 740, 758, 770, 785, 788, 809, 857, 866, 875, 878, 887, 890, 908, 944, 980, 1124, 1139, 1142, 1148, 1157, 1175, 1178, 1184, 1187, 1193, 1214, 1241, 1319, 1367, 1376, 1391, 1412, 1418, 1421

Offset: 1

Author

Reinhard Zumkeller, Sep 17 2009

Keywords

• base
• nonn

Comments

A165330(a(n)) = 407.

Examples

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

Crossrefs

Subsequence of A031179.

Cf. A046197, A035504, A008585, A165333.

Programs

Mathematica

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

Formula

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