cp's OEIS Frontend

A369871 a(n) = least prime factor of A024411(n).

%I A369871 #8 Feb 04 2024 18:29:38
%S A369871 2,2,3,2,3,2,2,3,2,3,2,5,2,3,3,2,2,5,3,2,2,3,5,2,2,2,3,2,3,5,2,7,2,3,
%T A369871 2,3,2,7,3,2,2,3,5,3,2,2,5,2,3,2,7,2,3,2,2,5,3,2,3,2,5,2,3,2,3,2,2,3,
%U A369871 7,2,5,3,2,3,5,2,7,3,2,3,2,3,2,5,2,3
%N A369871 a(n) = least prime factor of A024411(n).
%C A369871 Conjecture: every prime occurs infinitely many times.
%e A369871 Factorizations of for the first four terms of A024411 are given by
%e A369871 20 = 2 * 2 * 5; 28 = 2 * 2 * 7; 33 = 3 * 13; 36 = 2*2*3*3;
%e A369871 so that (a(1), a(2), a(3), a(4)) = (2, 2, 3, 2).
%e A369871 Corner of array whose n-th row shows the numbers n such that a(n) = n-th prime:
%e A369871    1    2    4    6    7    9   11
%e A369871    3    5    8   10   14   15   19
%e A369871   12   18   23   30   43   47   56
%e A369871   32   38   51   69   77   94  107
%t A369871 readOEISbFile[bNumber_] := ToExpression[ToString[Map[StringReplace[#,
%t A369871  FromCharacterCode[32] -> FromCharacterCode[44]] &,
%t A369871  Map[Most[#] &, Cases[Map[{#, StringFreeQ[StringTake[#, 1],
%t A369871  Except[Apply[Alternatives, Flatten[{Map[ToString[#] &, Range[10] - 1],
%t A369871  FromCharacterCode[45], FromCharacterCode[8722], "+"}]]]]} &,
%t A369871  Map[StringDrop[StringDrop[#, 1], -1] &, DeleteCases[
%t A369871  Map[ToString[{#}] &, Import[If[Head[bNumber] === Integer,
%t A369871  "http://oeis.org/" <> "A" <> # <> "/b" <> # <> ".txt" &[
%t A369871  StringTrim[StringReplace[ToString[PadLeft[IntegerDigits[bNumber], 6]],
%t A369871  FromCharacterCode[{44, 32}] -> ""], "{" | "}"]],
%t A369871  bNumber], "List"]], "{}"]]], {_, True}]]]]]
%t A369871 s = readOEISbFile["http://oeis.org/A024411/b024411.txt"];
%t A369871 (* s = 10000 terms of A024411 from b-file *)
%t A369871 t = Map[Last, s]; u = Take[t, 1000];
%t A369871 f[n_] := FactorInteger[n][[1, 1]]; Join[{1}, Array[f, 120, 2]]; v = Map[f, u]
%t A369871 (* _Peter J. C. Moses_, Feb 03 2024 *)
%Y A369871 Cf. A000040, A018252, A024411.
%K A369871 nonn
%O A369871 1,1
%A A369871 _Clark Kimberling_, Feb 03 2024