A113708 Limit set for operation of repeatedly replacing a number with the sum of the 4th power of its digits.

0, 1, 1138, 1634, 2178, 4179, 4338, 4514, 6514, 6725, 8208, 9219, 9474, 13139

Offset: 1

Author

Harvey P. Dale, Jan 17 2006

Keywords

• base
• full
• nonn
• fini

Comments

The trajectories under the given map terminate either at one of the fixed points 0, 1, 1634, 8208, 9474, or by reaching a member of the 2-cycle 2178 -> 6514 or the 7-cycle 1138 -> 4179 -> 9219 -> 13139 -> 6725 -> 4338 -> 4514.

Least k which returns a(n): 0, 1, 1138, 1346, 127, 8, 47, 3348, 66, 6725, 12, 1479, 4479, 2; and the number of iterations to get there are: 0, 0, 0, 1, 11, 3, 2, 1, 3, 0, 4, 1, 1, 18. - Robert G. Wilson v, Jan 24 2006

References

• Boris A. Kordemsky, The Moscow Puzzles, p. 160 (1972)

Crossrefs

Cf. A046156.

Programs

Mathematica

lst = {}; Do[a = NestWhile[Plus @@ (IntegerDigits@#^4)&, n, Unequal, All]; If[FreeQ[lst, a], AppendTo[lst, a]], {n, 6725}]; Union@lst (* Robert G. Wilson v, Jan 24 2006 *)

Extensions

Erroneous comment regarding the trajectory terminating conditions corrected by Ant King Jun 04 2013

Zero added to the set of least k’s which return a(n) for consistency with the first term of the given limit set. Similarly for the number of iterations required to get there, and two of the existing terms were corrected - Ant King Jun 07 2013