A099649 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.

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, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..72.

Example

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.
For n=32, list = {32,13,10,1,1,...}; max = 32 = n, so 32 is not in the sequence.
The sequence includes all positive integers < 145 except {1,10,13,23,31,32,44,100,103,109,129,130,133,139}.

Mathematica

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]

Crossrefs

Cf. A003132, A031176, A099646, A099649.

Sequence in context: A324280 A324281 A129946 * A330982 A033108 A049811

Adjacent sequences: A099646 A099647 A099648 * A099650 A099651 A099652

Keyword

base,nonn

Author

Labos Elemer, Nov 12 2004

Extensions

Edited by Jon E. Schoenfield, Nov 26 2017

Status

approved