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A242341
Numbers k such that k*10^k - 1 is a semiprime.
1
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
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.
Sequence in context: A006036 A308710 A376874 * A140738 A325593 A376373
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