A242273 -id:A242273 - cp's OEIS frontend

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

1, 6, 20, 29, 35, 40, 79, 164, 185, 198, 201, 218, 248, 249, 251, 264, 267, 274, 305, 323, 339, 344, 350, 362, 432, 539

Offset: 1

Vincenzo Librandi, May 12 2014

The semiprimes of this form are: 9, 5999999, 1999999999999999999999, 2899999999999999999999999999999, ...
From Robert Israel, Sep 04 2016: (Start)
k == 1 (mod 3) is in the sequence iff (k*10^k-1)/3 is prime.
The sequence includes 185, 198, 201, 251, 267, 274, and 1795. (End)
a(27) >= 596. Below 1000, 785 and 833 are in the sequence. Unknown factorization for 596, 669, 917, 933. - Hugo Pfoertner, Jul 29 2019

Status of 596*10^596-1 in factordb.com.

Cf. similar sequences listed in A242273.

Cf. A059671, A064756.

IsSemiprime:=func; [n: n in [2..70] | IsSemiprime(s) where s is n*10^n-1];

Maple

issemiprime:= proc(n) local F, t; F:= ifactors(n, easy)[2]; t:= add(f[2], f=F); if t = 1 then if type(F[1][1], integer) then return false fi elif t = 2 then return not hastype(F, name) else # t > 2 return false fi; F:= ifactors(n)[2]; return evalb(add(f[2], f=F)=2); end proc: select(t -> issemiprime(t*10^t-1), [$1..80]); # Robert Israel, Sep 04 2016

Mathematica

Select[Range[70], PrimeOmega[# 10^# - 1]==2&]

PARI

is(n)=bigomega(n*10^n-1)==2 \\ Charles R Greathouse IV, Sep 04 2016

Extensions

Terms 1 and 79 from Robert Israel, Sep 04 2016

a(8)-a(26) from Hugo Pfoertner, Jul 29 2019

cp's OEIS Frontend

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

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A259026 Numbers n such that n*23^n-1 is semiprime.