The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#8 by Michel Marcus at Mon Nov 27 03:23:03 EST 2017

STATUS

reviewed

approved

#7 by Joerg Arndt at Mon Nov 27 02:49:27 EST 2017

STATUS

proposed

reviewed

#6 by Jon E. Schoenfield at Sun Nov 26 15:50:21 EST 2017

STATUS

editing

proposed

Discussion

Mon Nov 27

02:49

Joerg Arndt: "trajectory" sounds OK, "orbit" being an alternative. "iteration" in name is not great, but let's leave it at that.

#5 by Jon E. Schoenfield at Sun Nov 26 15:49:11 EST 2017

NAME

Solutions to A099648[x](k) >x k, i.e. That is when , numbers such that the largest term in the iteration of the A003132() function strictly exceeds the initial value.

COMMENTS

Above 144 no more The last term I encountered was a(only 130) terms I could encounter= 144. Is this sequence finite[and full]? Is a(130) = 144 the final term?

EXAMPLE

For n=7: , the list= of values in the trajectory is {7,49,97,130,10,1,1,1,1,1,1,1,...} iv=7<; max = 130.So > 7 = n, so 7 is herein the sequence.

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

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

n=32: list={32,13,10,1,1,..}. So 32 is not here.

EXTENSIONS

Edited by Jon E. Schoenfield, Nov 26 2017

STATUS

approved

editing

Discussion

Sun Nov 26

15:50

Jon E. Schoenfield: The wording seemed to me to be in need of improvement.  Are these changes okay?  In particular, is "trajectory" a good word to use in the Example?  If so, would it be good to use it in the Name as well?

#4 by N. J. A. Sloane at Tue Oct 15 22:32:35 EDT 2013

AUTHOR

_Labos E. (labos(AT)ana.sote.hu), Elemer_, Nov 12 2004

Discussion

Tue Oct 15

22:32

OEIS Server: https://oeis.org/edit/global/2029

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

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]

KEYWORD

base,nonn,new

#2 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

KEYWORD

base,nonn,new

AUTHOR

Labos E. (labos(AT)ana1ana.sote.hu), Nov 12 2004

#1 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

NAME

Solutions to A099648[x]>x. That is when the largest term in iteration of A003132() function strictly exceeds the initial value.

DATA

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

Above 144 no more (only 130) terms I could encounter. Is this sequence finite[and full]?

EXAMPLE

n=7: list={7,49,97,130,10,1,1,1,1,1,1,1,..} iv=7<max=130.So 7 is here.

numbers <145 are here except {1,10,13,23,31,32,44,100,103,109,129,130,133,139}.

n=32: list={32,13,10,1,1,..}. So 32 is not here.

MATHEMATICA

CROSSREFS

Cf. A003132, A031176, A099646, A099649.

KEYWORD

base,nonn

AUTHOR

Labos E. (labos(AT)ana1.sote.hu), Nov 12 2004

STATUS

approved