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Solutions to A099648(k) > k, i.e., numbers such that the largest term in the iteration of the A003132() function strictly exceeds the initial value.
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%I #8 Nov 27 2017 03:23:03

%S 2,3,4,5,6,7,8,9,11,12,14,15,16,17,18,19,20,21,22,24,25,26,27,28,29,

%T 30,33,34,35,36,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,54,55,

%U 56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79

%N Solutions to A099648(k) > k, i.e., numbers such that the largest term in the iteration of the A003132() function strictly exceeds the initial value.

%C The last term I encountered was a(130) = 144. Is this sequence finite? Is a(130) = 144 the final term?

%e For n=7, the list of values in the trajectory is {7,49,97,130,10,1,1,1,1,1,1,1,...}; max = 130 > 7 = n, so 7 is in the sequence.

%e For n=32, list = {32,13,10,1,1,...}; max = 32 = n, so 32 is not in the sequence.

%e The sequence includes all positive integers < 145 except {1,10,13,23,31,32,44,100,103,109,129,130,133,139}.

%t ed[x_] :=IntegerDigits[x]; func[x_] :=Apply[Plus, ed[x]^2]; itef[x_, ho_] :=NestList[id2, x, 100]; ta={{0}};Do[s=Max[Union[itef[w, 100]]]; If[Greater[s, w], Print[w];ta=Append[ta, w]], {w, 1, 10000000}]; Delete[ta, 1]

%Y Cf. A003132, A031176, A099646, A099649.

%K base,nonn

%O 1,1

%A _Labos Elemer_, Nov 12 2004

%E Edited by _Jon E. Schoenfield_, Nov 26 2017