A035504 Numbers that eventually reach 1 under "x -> sum of cubes of digits of x".

1, 10, 100, 112, 121, 211, 778, 787, 877, 1000, 1012, 1021, 1102, 1120, 1189, 1198, 1201, 1210, 1234, 1243, 1324, 1342, 1423, 1432, 1579, 1597, 1759, 1795, 1819, 1891, 1918, 1957, 1975, 1981, 2011, 2101, 2110, 2134, 2143, 2314, 2341, 2413, 2431, 2779

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

Comments

Subsequence of A016777; a(n) mod 3 = 1; A165330(a(n))=1. [Reinhard Zumkeller, Sep 17 2009]

References

• R. K. Guy, Unsolved Problems Number Theory, Sect. E34.

Links

• R. Zumkeller, Table of n, a(n) for n = 1..1000
• R. Styer, Smallest Examples of Strings of Consecutive Happy Numbers, J. Int. Seq. 13 (2010), 10.6.3, Section 4.

Crossrefs

Cf. A007770.

Cf. A046197, A008585, A165333, A165334, A165335; subsequence of A031179.

Programs

Mathematica

f[n_]:=Plus@@(IntegerDigits[n]^3);Trajectory[n_] := Most[NestWhileList[f, n, UnsameQ, All]];Select[Range[2780],Last[Trajectory[#]]==1 &] (* Ant King, May 24 2013 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 31 2000