A361503 - OEIS

A361503

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

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, 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, 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

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OFFSET

1,1

COMMENTS

Understanding this sequence is the key to analyzing A359804.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..16383

EXAMPLE

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.

MATHEMATICA

nn = 120; c[_] = False; q[_] = 1;

Array[Set[{a[#], c[#]}, {#, True}] &, 2];

Set[{i, j}, {a[1], a[2]}]; u = 3;

{2}~Join~Reap[Do[

(k = q[#]; While[c[k #], k++]; k *= #;

While[c[# q[#]], q[#]++]) &[(p = 2;

While[Divisible[i j, p], p = NextPrime[p]]; p)]; Sow[p];

Set[{a[n], c[k], i, j}, {k, True, j, k}];

If[k == u, While[c[u], u++]], {n, 3, nn}] ][[-1, -1]] (* Michael De Vlieger, Mar 18 2023 *)

CROSSREFS

Cf. A053669, A359804.