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].

35, 36, 46, 53, 57, 63, 64, 75, 135, 138, 153, 156, 165, 183, 237, 245, 246, 254, 264, 273, 279, 297, 305, 306, 315, 318, 327, 334, 343, 347, 350, 351, 360, 372, 374, 381, 388, 406, 425, 426, 433, 437, 452, 460, 462, 473, 503, 507, 513, 516, 524, 530, 531

Offset: 1

Author

Labos Elemer, Nov 11 2004

Keywords

• base
• nonn

Comments

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.

Examples

			n=35 is here because list={36,46,53,[35],35,...} with transient t=3, c=1 cycle-length.
		

Crossrefs

Cf. A031176, A099645, A007770, A099646.

Programs

Mathematica

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[tmc-(c1-1), 1]]