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A361503 a(1)=2; thereafter a(n) = smallest prime that does not divide b(n-1)*b(n), where b(k) = A359804(k).

%I A361503 #15 Mar 19 2023 10:20:26
%S A361503 2,3,5,2,3,5,7,3,2,5,7,11,3,5,7,11,5,3,7,5,11,7,2,3,5,7,11,5,7,2,3,5,
%T A361503 7,3,5,7,2,5,7,11,13,5,2,3,5,2,7,3,5,7,11,5,3,2,5,7,11,2,5,3,7,5,3,7,
%U A361503 2,11,3,7,5,3,7,5,11,7,5,11,7,5,3,7,11,3,2,5,7,2,5,3,2,5,7,13,3,5,2,3
%N A361503 a(1)=2; thereafter a(n) = smallest prime that does not divide b(n-1)*b(n), where b(k) = A359804(k).
%C A361503 Understanding this sequence is the key to analyzing A359804.
%H A361503 Michael De Vlieger, <a href="/A361503/b361503.txt">Table of n, a(n) for n = 1..16383</a>
%e A361503 b(1)=1, b(2)=2, b(3)=3, b(4)=5, so a(2) = smallest prime not dividing 2, which is 3. a(3) = smallest prime not dividing 2*3, which is 5, and a(4) = smallest prime not dividing 3*5, which is 2.
%t A361503 nn = 120; c[_] = False; q[_] = 1;
%t A361503 Array[Set[{a[#], c[#]}, {#, True}] &, 2];
%t A361503 Set[{i, j}, {a[1], a[2]}]; u = 3;
%t A361503 {2}~Join~Reap[Do[
%t A361503      (k = q[#]; While[c[k #], k++]; k *= #;
%t A361503         While[c[# q[#]], q[#]++]) &[(p = 2;
%t A361503        While[Divisible[i j, p], p = NextPrime[p]]; p)]; Sow[p];
%t A361503      Set[{a[n], c[k], i, j}, {k, True, j, k}];
%t A361503 If[k == u, While[c[u], u++]], {n, 3, nn}] ][[-1, -1]] (* _Michael De Vlieger_, Mar 18 2023 *)
%Y A361503 Cf. A053669, A359804.
%K A361503 nonn
%O A361503 1,1
%A A361503 _N. J. A. Sloane_, Mar 18 2023