A099647 - OEIS

A099647

Function f[n]=1+Sum[digit^2 of n] is iterated as in A099646. Values x for which A099646[x]=1 are listed here. These terms are analogous to happy-numbers [=A007770].

%I #4 Oct 15 2013 22:32:35

%S 35,36,46,53,57,63,64,75,135,138,153,156,165,183,237,245,246,254,264,

%T 273,279,297,305,306,315,318,327,334,343,347,350,351,360,372,374,381,

%U 388,406,425,426,433,437,452,460,462,473,503,507,513,516,524,530,531

%N Function f[n]=1+Sum[digit^2 of n] is iterated as in A099646. Values x for which A099646[x]=1 are listed here. These terms are analogous to happy-numbers [=A007770].

%C Iteration g[x] applied in A031176 is slightly modified to obtain actual function to iterate here: f[x]=1+g[x].Initial values resulting in fixed points are collected.

%e n=35 is here because list={36,46,53,[35],35,...} with transient t=3,

%e c=1 cycle-length;

%t 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}]; Flatten[Position[c1, 1]]

%Y Cf. A031176, A099645, A007770, A099646.

%K base,nonn

%O 1,1

%A _Labos Elemer_, Nov 11 2004