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

1,2

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

Cf. A373902, A000040.

Sequence in context: A260564 A107126 A373444 * A247091 A025122 A173684

Adjacent sequences: A371615 A371616 A371617 * A371619 A371620 A371621

Keyword

nonn

Author

Scott R. Shannon, Jun 22 2024

Status

approved