OFFSET
1,2
COMMENTS
For the terms studied, in the list of primes' first appearance, they appear in their natural order.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..826 (terms 1..178 from Scott R. Shannon)
MATHEMATICA
nn = 45000; c[_] := {}; p[_] := False; a[1] = j = 2; c[2] = {2}; p[2] = 1;
{p[2]}~Join~Monitor[Reap[
Do[If[PrimePowerQ[j],
(k = 1;
While[Or[j == # k, CoprimeQ[j, # k], ! FreeQ[c[j], # k]], k++];
k *= #) &[FactorInteger[j][[1, 1]]],
k = FactorInteger[j][[1, 1]];
While[Or[j == k, CoprimeQ[j, k], ! FreeQ[c[j], k]], k++] ];
If[PrimeQ[k], If[! p[k], Sow[n]; p[k] = True]];
Set[{a[n], c[j], c[k], j},
{k, Union[c[j], {k}], Union[c[k], {j}], k}], {n, 2, nn}] ][[-1, 1]], n] (* Michael De Vlieger, Jun 22 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jun 22 2024
STATUS
approved