|
| |
|
|
A120685
|
|
Let f(0)=m; f(n+1)=1+lpf(f(n)), where lpf(n) is the largest prime factor of n (A006530). For any m, for sufficiently large n the sequence f(n) oscillates between 3 and 4. Given a sufficently large n, this allows us to divide integers in two classes: C3 (m such that f(n)=3) and C4 (m such that f(n)=4). Note that then for n+1 the ones that belong to C3 will belong to C4 and vice-versa. Anyhow the two classes are independent of n. We present here C4 as the one that includes 4. In A120684 we present C3 as the one that includes 3.
|
|
4
| |
|
|
2, 4, 5, 8, 10, 11, 13, 15, 16, 17, 20, 22, 23, 25, 26, 30, 32, 33, 34, 37, 39, 40, 41, 44, 45, 46, 47, 50, 51, 52, 53, 55, 60, 61, 64, 65, 66, 68, 69, 71, 74, 75, 77, 78, 80, 82, 83, 85, 88, 90, 91, 92, 94, 97, 99, 100, 102, 104, 106, 107, 110, 111, 113, 115, 117, 119, 120
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
EXAMPLE
| Oscillation between 3 and 4: 1+lpf(3)=1+3=4; 1+lpf(4)=1+2=3;
Other value, e.g. 7: 1+lpf(7)=1+7=8; 1+lpf(8)=1+2=3 (7 belongs to C3)
Other value, e.g. 20: 1+lpf(10)=1+5=6; 1+lpf(6)=1+3=4 (20 belongs to C4).
|
|
|
MATHEMATICA
| f = Function[n, FactorInteger[n][[ -1, 1]] + 1]; mn = Map[(NestList[f, #, 8][[ -1]]) &, Range[2, 500]]; out = Flatten[Position[mn, 4]] + 1
|
|
|
CROSSREFS
| Cf. A120684, A072268, A006530.
Sequence in context: A026138 A026170 A026174 * A160545 A161790 A131396
Adjacent sequences: A120682 A120683 A120684 * A120686 A120687 A120688
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Carlos Alves (cjsalves(AT)gmail.com), Jun 25 2006
|
| |
|
|
