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A369871
a(n) = least prime factor of A024411(n).
0
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, 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, 7, 2, 5, 3, 2, 3, 5, 2, 7, 3, 2, 3, 2, 3, 2, 5, 2, 3
OFFSET
1,1
COMMENTS
Conjecture: every prime occurs infinitely many times.
EXAMPLE
Factorizations of for the first four terms of A024411 are given by
20 = 2 * 2 * 5; 28 = 2 * 2 * 7; 33 = 3 * 13; 36 = 2*2*3*3;
so that (a(1), a(2), a(3), a(4)) = (2, 2, 3, 2).
Corner of array whose n-th row shows the numbers n such that a(n) = n-th prime:
1 2 4 6 7 9 11
3 5 8 10 14 15 19
12 18 23 30 43 47 56
32 38 51 69 77 94 107
MATHEMATICA
readOEISbFile[bNumber_] := ToExpression[ToString[Map[StringReplace[#,
FromCharacterCode[32] -> FromCharacterCode[44]] &,
Map[Most[#] &, Cases[Map[{#, StringFreeQ[StringTake[#, 1],
Except[Apply[Alternatives, Flatten[{Map[ToString[#] &, Range[10] - 1],
FromCharacterCode[45], FromCharacterCode[8722], "+"}]]]]} &,
Map[StringDrop[StringDrop[#, 1], -1] &, DeleteCases[
Map[ToString[{#}] &, Import[If[Head[bNumber] === Integer,
"http://oeis.org/" <> "A" <> # <> "/b" <> # <> ".txt" &[
StringTrim[StringReplace[ToString[PadLeft[IntegerDigits[bNumber], 6]],
FromCharacterCode[{44, 32}] -> ""], "{" | "}"]],
bNumber], "List"]], "{}"]]], {_, True}]]]]]
s = readOEISbFile["http://oeis.org/A024411/b024411.txt"];
(* s = 10000 terms of A024411 from b-file *)
t = Map[Last, s]; u = Take[t, 1000];
f[n_] := FactorInteger[n][[1, 1]]; Join[{1}, Array[f, 120, 2]]; v = Map[f, u]
(* Peter J. C. Moses, Feb 03 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 03 2024
STATUS
approved