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Search: id:A099646
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| A099646 |
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Function f[n]=1+Sum[digit^2 of n] is iterated and a[n] is the length of terminal cycle at initial value n. |
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+0
5
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| 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Iteration g[x] applied in A031176 is slightly modified to obtain actual function: f[x]=1+g[x]. Cases of a[n]=1 (n=35,36,...) are analogous to happy numbers [A007770].
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EXAMPLE
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n=1:iteration-list=
{1,2,5,26,41,18,66,73,59,107,51,[27,54,42,21,6,37,59,107,51],27...
with t=11 transient and c=a[1]=9, the cycle-length;
n=35:list={36,46,53,[35],35,...} with transient t=3,c=1 cycle-length.
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MATHEMATICA
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ed[x_] :=IntegerDigits[x]; f[x_] :=Apply[Plus, ed[x]^2]+1; itef[x_, ho_] :=NestList[f, x, ho]; tmc=Table[Length[Union[itef[w, 100], {w, 1, 256}]; c1=Table[Min[Flatten[Position[itef[w, Length[Union[itef[w, 100]]]] -Last[itef[w, Length[Union[itef[w, 100]]]]], 0]]], {w, 1, 256}]; (*transient-length=*)c1-1; (*cycle-length=*)c=tmc-(c1-1); (*ho=iteration number is chosen by trial and error*) (*program provides t, t+c and c lengths[=unknown-in-advance] for any similar iterations if f modified*)
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CROSSREFS
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Cf. A031176, A099645, A007770, A099647.
Sequence in context: A091668 A116667 A137577 this_sequence A010734 A066568 A106326
Adjacent sequences: A099643 A099644 A099645 this_sequence A099647 A099648 A099649
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KEYWORD
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nonn,base
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 11 2004
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