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Limit set for operation of repeatedly replacing a number with the sum of the 4th power of its digits.
1

%I #13 Mar 31 2017 21:12:25

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

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

%C 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.

%C 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

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

%t 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 *)

%Y Cf. A046156.

%K base,full,nonn,fini

%O 1,3

%A _Harvey P. Dale_, Jan 17 2006

%E Erroneous comment regarding the trajectory terminating conditions corrected by _Ant King_ Jun 04 2013

%E 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