A066105 Indices of the maximum increasing subsequences of A066848 and A066849.
1, 2, 3, 4, 9, 10, 13, 16, 27, 35, 39, 40, 44, 55, 56, 63, 66
Offset: 0
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After 5, 7 is the next member and not 6 as 6*1 = 2*3.
import qualified Data.Set as Set (null)
import Data.Set as Set (empty, insert, member)
a066720 n = a066720_list !! (n-1)
a066720_list = f [] 1 empty where
f ps z s | Set.null s' = f ps (z + 1) s
| otherwise = z : f (z:ps) (z + 1) s'
where s' = g (z:ps) s
g [] s = s
g (x:qs) s | (z * x) `member` s = empty
| otherwise = g qs $ insert (z * x) s
-- Reinhard Zumkeller, Nov 19 2013
A[1]:= 1:
F:= {1}:
for n from 2 to 100 do
for k from A[n-1]+1 do
Fk:= {k^2, seq(A[i]*k,i=1..n-1)};
if Fk intersect F = {} then
A[n]:= k;
F:= F union Fk;
break
fi
od
od:
seq(A[i],i=1..100); # Robert Israel, Mar 02 2016
s={1}; xok := Module[{}, For[i=1, i<=n, i++, For[j=1; k=Length[dl=Divisors[s[[i]]x]], j<=k, j++; k--, If[MemberQ[s, dl[[j]]]&&MemberQ[s, dl[[k]]], Return[False]]]]; True]; For[n=1, True, n++, Print[s[[n]]]; For[x=s[[n]]+1, True, x++, If[xok, AppendTo[s, x]; Break[]]]] (* Dean Hickerson *)
a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, b = c = Table[a[i], {i, 1, n - 1}], d}, While[c = Append[b, k]; Length[ Union[ Flatten[ Table[ c[[i]]/c[[j]], {i, 1, n}, {j, 1, n}]]]] != n^2 - n + 1, k++ ]; Return[k]]; Table[ a[n], {n, 1, 75} ] (* Robert G. Wilson v *)
nmax = 100; a[1] = 1; F = {1};
For[n = 2, n <= nmax, n++,
For[k = a[n-1]+1, True, k++, Fk = Join[{k^2}, Table[a[i]*k, {i, 1, n-1}]] // Union; If[Fk ~Intersection~ F == {}, a[n] = k; F = F ~Union~ Fk; Break[]
]]];
Array[a, nmax] (* Jean-François Alcover, Mar 26 2019, after Robert Israel *)
{a066720(m) = local(a,rat,n,s,new,b,i,k,j); a=[]; rat=Set([]); n=0; s=0; while(sKlaus Brockhaus, Feb 23 2002
3/4 does not occur until we reach A066720(401) = 2436 and then we see A066720(320)/A066720(401) = 1827/2436 = 3/4. Therefore a(4) = 2436.
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