A026433 a(n) = least positive integer > a(n-1) and not a(i)*a(j)-1 for 1<=i

2, 3, 4, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 22, 24, 28, 30, 32, 33, 34, 36, 37, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 61, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Contains all members of A006093 except 1. - Robert Israel, Mar 06 2016

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A026431 and references therein.

Cf. A006093.

Programs

Maple

N:= 1000: # to get all terms <= N
V:= Vector(N):
a[1]:= 2: finished:= false:
for n from 2  do
  for i from a[n-1]+1 do
    if i > N then
      finished:= true; break
    elif V[i] = 0 then break
    fi
  od:
  if finished then break fi;
  a[n]:= i;
  S:= select(`<=`,[seq(a[j]*i-1,j=1..n-1)],N);
  if S <> [] then V[S]:= 1 fi;
od:
seq(a[i],i=1..n-1); # Robert Israel, Mar 06 2016

Mathematica

a = {2, 3}; used = {a[[1]]*a[[2]] - 1}; Do[k = a[[-1]] + 1; While[MemberQ[used, k], k++]; used = Union[used, k*a - 1]; AppendTo[a, k], {n, 3, 60}]; a (* Ivan Neretin, Mar 06 2016 *)

Extensions

Name clarified by Robert C. Lyons, Feb 06 2025