# Generate A065825

## Pyth, 17 bytes

```
ff!/#.OZ.cY3.cSTQ
```

Try it online!

`.cSTQ`

: generate all list of numbers in the range [1,T] with length equal to the input.

`.cY3`

: for each of those, generate all length 3 subsequences.

`/#.OZ`

: filter for the subsequences where the average is a member of the list. These are the arithmetic progressions.

`f!`

: filter for the original lists with no arithmetic progressions

`f`

: find the lowest T where at least one list is found.

## Python 3.8, ~~123~~ ~~115~~ ~~96~~ 94 bytes

Another ~~-15~~ -17 bytes thanks to Surcolose Sputum!

```
f=lambda n,k=1:len(d:=f'{k:b}')*all(k>>i&k&k<<i<1for i in range(d.count('1')//n,k))or f(n,k+1)
```

Try it online!

## Python 2, ~~147~~ ~~135~~ 124 bytes

-11 bytes thanks to Surcolose Sputum!

```
from itertools import*
f=lambda n,k=1,C=combinations:k*any(all(a+c-b*2for a,b,c in C(w,3))for w in C(range(k),n))or f(n,k+1)
```

Try it online!

## R, ~~96~~ 83 bytes

```
k=n=scan();C=combn;`[`=Map;try(while(!any(all[diff[C[C(1:k,n,,F),3],1,2]]))k=k+1);k
```

Try it online!

Full program, returns 1-indexed member of the sequence. Very slow for `n > 8`

.