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

1,2

Comments

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

Links

Table of n, a(n) for n=1..26.

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

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&]

Prog

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

Crossrefs

Cf. similar sequences listed in A242273.

Cf. A059671, A064756.

Sequence in context: A064771 A006036 A308710 * A140738 A325593 A226363

Adjacent sequences: A242338 A242339 A242340 * A242342 A242343 A242344

Keyword

nonn,more,hard

Author

Vincenzo Librandi, May 12 2014

Extensions

Terms 1 and 79 from Robert Israel, Sep 04 2016

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

Status

approved