login
Fixed points or cycle values for sequences of the form s(k+1)=sopfr(2s(k)+1), with sopfr=A001414 and any s(1).
3

%I #3 Sep 24 2013 00:41:43

%S 10,14,24,29,59

%N Fixed points or cycle values for sequences of the form s(k+1)=sopfr(2s(k)+1), with sopfr=A001414 and any s(1).

%C A136136 starts with s(1)=1 and ends in 10 as fixed point.

%C For s(1) from 1 to 10000 either (a) the sequence converges to 10, the fixed point; or (b) it cycles - between 14, 29, 59 and 24.

%e s(1)=1; ... s(6)=12; s(7)=sopfr(2*12+1)=5+5=10; s(8)=sopfr(2*10+1)=3+7=10

%e s(1)=1 leads to 10 as fixed point.

%e s(1)=2; ... s(7)=24; s(8)=14; s(9)=29; s(10)=59; s(11)=24

%e s(1)=2 leads to the cycle (24 14 29 59).

%t sopfr = Function[x, Plus @@ Map[Times @@ # &, FactorInteger[x]]]; Union[Table[NestList[sopfr[2# + 1] &, s0, 100][[ -1]], {s0, 1, 10000}]]

%Y Cf. A136136.

%K nonn

%O 1,1

%A _Carlos Alves_, Dec 20 2007