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Numbers n such that n*9^n+1 is semiprime.
1

%I #14 Sep 08 2022 08:46:08

%S 1,8,12,16,20,50,208,254,282,342,350,386

%N Numbers n such that n*9^n+1 is semiprime.

%C The semiprimes of this form are: 10, 344373769, 3389154437773, 29648323021629457, 243153309181138576021, ...

%C a(13) >= 512. - _Hugo Pfoertner_, Aug 05 2019

%H factordb.com, <a href="http://factordb.com/index.php?query=9%5E512*512%2B1">Status of 512*9^512+1</a>.

%t Select[Range[70], PrimeOmega[# 9^# + 1] == 2 &]

%o (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [1..70] | IsSemiprime(s) where s is n*9^n+1];

%Y Cf. similar sequences listed in A242203.

%Y Cf. A064747.

%K nonn,more,hard

%O 1,2

%A _Vincenzo Librandi_, May 10 2014

%E a(7)-a(12) from _Hugo Pfoertner_, Aug 05 2019