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a(n) = least positive integer > a(n-1) and not a(i)*a(j)-1 for 1<=i<j<=n, with initial terms 1,3.
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%I #14 Feb 06 2025 13:51:05

%S 1,3,4,5,6,7,8,9,10,12,13,15,16,18,21,22,24,25,28,30,32,33,36,37,40,

%T 42,43,45,46,48,50,52,54,56,57,58,60,61,66,67,68,70,72,73,75,76,78,80,

%U 81,82,84,85,86,88,91,92,93,94,96,97

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

%H Ivan Neretin, <a href="/A026432/b026432.txt">Table of n, a(n) for n = 1..1000</a>

%t a = {1, 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 Cf. A026431 and references therein.

%K nonn,changed

%O 1,2

%A _Clark Kimberling_

%E Name clarified by _Robert C. Lyons_, Feb 06 2025