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%I #26 Sep 08 2022 08:46:03
%S 201,500001,130000000000001,280000000000000000000000000001,
%T 340000000000000000000000000000000001,
%U 36000000000000000000000000000000000001,39000000000000000000000000000000000000001
%N Semiprimes of the form n*10^n + 1.
%C This is to A216347 as semiprimes A001358 are to primes A000040. The corresponding n are 2, 5, 13, 28, 34, 36, 39, ... (A216378).
%C a(14) >= 414*10^414 + 1. - _Hugo Pfoertner_, Jul 28 2019
%H Hugo Pfoertner, <a href="/A216376/b216376.txt">Table of n, a(n) for n = 1..13</a>
%F semiprimes in A064748.
%e a(1) = 2 * 10^2 + 1 = 201 = 3 * 67.
%e a(2) = 5 * 10^5 + 1 = 500001 = 3 * 166667.
%e a(3) = 13*10^13 + 1 = 130000000000001 = 6529 * 19911165569.
%e a(4) = 28 * 10^28 + 1 = 29 * 9655172413793103448275862069.
%t SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Table[n*10^n + 1, {n, 50}], SemiPrimeQ[#] &] (* _T. D. Noe_, Sep 07 2012 *)
%t Select[Table[n*10^n + 1, {n, 50}], PrimeOmega[#] == 2&] (* _Vincenzo Librandi_, Sep 22 2012 *)
%o (Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..40] | IsSemiprime(s) where s is n*10^n + 1]; // _Vincenzo Librandi_, Sep 22 2012
%Y Cf. A001358, A064748, A216347, A216378.
%K nonn,hard
%O 1,1
%A _Jonathan Vos Post_, Sep 06 2012
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