A136197 Fixed points or cycle values for sequences of the form s(k+1)=sopfr(2s(k)+1), with sopfr=A001414 and any s(1).

10, 14, 24, 29, 59

Offset

1,1

Comments

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

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.

Links

Table of n, a(n) for n=1..5.

Example

s(1)=1; ... s(6)=12; s(7)=sopfr(2*12+1)=5+5=10; s(8)=sopfr(2*10+1)=3+7=10
s(1)=1 leads to 10 as fixed point.
s(1)=2; ... s(7)=24; s(8)=14; s(9)=29; s(10)=59; s(11)=24
s(1)=2 leads to the cycle (24 14 29 59).

Mathematica

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

Crossrefs

Cf. A136136.

Sequence in context: A286843 A069207 A168671 * A071620 A175664 A053690

Adjacent sequences: A136194 A136195 A136196 * A136198 A136199 A136200

Keyword

nonn

Author

Carlos Alves, Dec 20 2007

Status

approved