A371618 Indices where prime(n) first appears in A373902.

1, 10, 14, 44, 108, 135, 209, 252, 401, 840, 890, 1197, 1446, 1678, 1810, 2408, 2796, 3207, 3799, 4212, 4716, 5246, 5590, 6617, 8042, 8564, 9253, 9845, 10549, 12447, 14768, 15328, 16820, 17368, 18876, 21480, 22798, 24802, 26142, 27567, 28511, 29373, 32550, 33416, 35010, 35852, 40976, 43945

Offset: 1

Author

Scott R. Shannon, Jun 22 2024

Keywords

• nonn

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..887 (terms 1..178 from Scott R. Shannon)

Crossrefs

Cf. A373902, A000040.

Programs

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 *)