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A026433 a(n) = least positive integer > a(n-1) and not a(i)*a(j)-1 for 1<=i with initial terms 2,3.

%I A026433 #17 Feb 06 2025 13:51:09
%S A026433 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,
%T A026433 44,45,46,48,49,50,52,54,56,57,58,60,61,64,66,68,69,70,72,74,75,76,78,
%U A026433 80,81,82,84,85,86,88,90,92,93,94,96
%N A026433 a(n) = least positive integer > a(n-1) and not a(i)*a(j)-1 for 1<=i<j<=n, with initial terms 2,3.
%C A026433 Contains all members of A006093 except 1. - _Robert Israel_, Mar 06 2016
%H A026433 Ivan Neretin, <a href="/A026433/b026433.txt">Table of n, a(n) for n = 1..1000</a>
%p A026433 N:= 1000: # to get all terms <= N
%p A026433 V:= Vector(N):
%p A026433 a[1]:= 2: finished:= false:
%p A026433 for n from 2  do
%p A026433   for i from a[n-1]+1 do
%p A026433     if i > N then
%p A026433       finished:= true; break
%p A026433     elif V[i] = 0 then break
%p A026433     fi
%p A026433   od:
%p A026433   if finished then break fi;
%p A026433   a[n]:= i;
%p A026433   S:= select(`<=`,[seq(a[j]*i-1,j=1..n-1)],N);
%p A026433   if S <> [] then V[S]:= 1 fi;
%p A026433 od:
%p A026433 seq(a[i],i=1..n-1); # _Robert Israel_, Mar 06 2016
%t A026433 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 *)
%Y A026433 Cf. A026431 and references therein.
%Y A026433 Cf. A006093.
%K A026433 nonn
%O A026433 1,1
%A A026433 _Clark Kimberling_
%E A026433 Name clarified by _Robert C. Lyons_, Feb 06 2025