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%I #27 Sep 08 2022 08:46:21
%S 4,5,6,7,8,19,31,53,67,293,586,641,922,2137,3011
%N Numbers k such that 10^k + 1 is a semiprime.
%C a(16) > 12000.
%C 10^k + 1 is composite unless k is a power of 2, and it can be conjectured that it is composite for all k > 2, cf. A038371 and A185121. - _M. F. Hasler_, Jul 30 2019
%C Suppose k is odd. Then k is a term if and only if (10^k+1)/11 is prime. - _Chai Wah Wu_, Jul 31 2019
%e a(1) = 4 because 10^4 + 1 = 10001 = 73*137.
%t Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* _Vincenzo Librandi_, Jul 31 2019 *)
%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // _Vincenzo Librandi_, Jul 31 2019
%Y Cf. A003021, A038371, A046413, A057934, A062397, A092559.
%Y Odd terms in sequence: A001562.
%K nonn,more,hard
%O 1,1
%A _Hugo Pfoertner_, Jul 29 2019
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