cp's OEIS Frontend

A242341 Numbers k such that k*10^k - 1 is a semiprime.

%I A242341 #21 Sep 08 2022 08:46:08
%S A242341 1,6,20,29,35,40,79,164,185,198,201,218,248,249,251,264,267,274,305,
%T A242341 323,339,344,350,362,432,539
%N A242341 Numbers k such that k*10^k - 1 is a semiprime.
%C A242341 The semiprimes of this form are: 9, 5999999, 1999999999999999999999, 2899999999999999999999999999999, ...
%C A242341 From _Robert Israel_, Sep 04 2016: (Start)
%C A242341 k == 1 (mod 3) is in the sequence iff (k*10^k-1)/3 is prime.
%C A242341 The sequence includes 185, 198, 201, 251, 267, 274, and 1795. (End)
%C A242341 a(27) >= 596. Below 1000, 785 and 833 are in the sequence. Unknown factorization for 596, 669, 917, 933. - _Hugo Pfoertner_, Jul 29 2019
%H A242341 <a href="http://factordb.com/index.php?query=596*10%5E596-1">Status of 596*10^596-1 in factordb.com</a>.
%p A242341 issemiprime:= proc(n) local F, t;
%p A242341     F:= ifactors(n, easy)[2];
%p A242341     t:= add(f[2], f=F);
%p A242341     if t = 1 then
%p A242341        if type(F[1][1], integer) then return false fi
%p A242341     elif t = 2 then
%p A242341        return not hastype(F, name)
%p A242341     else # t > 2
%p A242341        return false
%p A242341     fi;
%p A242341     F:= ifactors(n)[2];
%p A242341     return evalb(add(f[2], f=F)=2);
%p A242341 end proc:
%p A242341 select(t -> issemiprime(t*10^t-1), [$1..80]); # _Robert Israel_, Sep 04 2016
%t A242341 Select[Range[70], PrimeOmega[# 10^# - 1]==2&]
%o A242341 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..70] | IsSemiprime(s) where s is n*10^n-1];
%o A242341 (PARI) is(n)=bigomega(n*10^n-1)==2 \\ _Charles R Greathouse IV_, Sep 04 2016
%Y A242341 Cf. similar sequences listed in A242273.
%Y A242341 Cf. A059671, A064756.
%K A242341 nonn,more,hard
%O A242341 1,2
%A A242341 _Vincenzo Librandi_, May 12 2014
%E A242341 Terms 1 and 79 from _Robert Israel_, Sep 04 2016
%E A242341 a(8)-a(26) from _Hugo Pfoertner_, Jul 29 2019