A299383
Numbers k such that k * 20^k - 1 is prime.
Original entry on oeis.org
1, 18, 44, 60, 80, 123, 429, 1166, 2065, 8774, 35340, 42968, 50312, 210129
Offset: 1
Numbers n such that n * b^n - 1 is prime:
A008864 (b=1),
A002234 (b=2),
A006553 (b=3),
A086661 (b=4),
A059676 (b=5),
A059675 (b=6),
A242200 (b=7),
A242201 (b=8),
A242202 (b=9),
A059671 (b=10),
A299374 (b=11),
A299375 (b=12),
A299376 (b=13),
A299377 (b=14),
A299378 (b=15),
A299379 (b=16),
A299380 (b=17),
A299381 (b=18),
A299382 (b=19), this sequence (b=20).
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[n: n in [1..10000] |IsPrime(n*20^n-1)];
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Select[Range[1, 10000], PrimeQ[n*20^n-1] &]
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for(n=1, 10000, if(isprime(n*20^n-1), print1(n", ")))
A242341
Numbers k such that k*10^k - 1 is a semiprime.
Original entry on oeis.org
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
Cf. similar sequences listed in
A242273.
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IsSemiprime:=func; [n: n in [2..70] | IsSemiprime(s) where s is n*10^n-1];
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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
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Select[Range[70], PrimeOmega[# 10^# - 1]==2&]
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is(n)=bigomega(n*10^n-1)==2 \\ Charles R Greathouse IV, Sep 04 2016
A216346
Primes of the form n*10^n - 1.
Original entry on oeis.org
199, 2999, 799999999, 1099999999999, 14999999999999999, 38999999999999999999999999999999999999999, 59999999999999999999999999999999999999999999999999999999999999, 71999999999999999999999999999999999999999999999999999999999999999999999999
Offset: 1
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lst={}; Do[ p=n*10^n- 1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 60}]; lst
Select[Table[n*10^n-1,{n,100}],PrimeQ] (* Harvey P. Dale, Sep 17 2023 *)
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