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Numbers k such that the number k11 is prime.
4

%I #30 Nov 03 2024 02:14:39

%S 0,2,3,8,9,15,18,20,21,23,24,27,30,35,39,41,42,50,57,60,62,63,69,72,

%T 74,80,81,83,90,93,95,98,101,102,107,113,114,120,122,125,126,129,134,

%U 137,140,144,155,161,164,168,170,179,182,183,189,192,200,204,206,210,212

%N Numbers k such that the number k11 is prime.

%C k such that 100*k+11 is prime. - _Robert Israel_, Jul 30 2015

%H Robert Israel, <a href="/A101471/b101471.txt">Table of n, a(n) for n = 1..10000</a>

%H Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The first 1,000 primes</a>.

%e If k=2, then k11 = 211 (prime);

%e If k=50, then k11 = 5011 (prime);

%e If k=98, then k11 = 9811 (prime).

%p select(t -> isprime(100*t+11), [$0..1000]); # _Robert Israel_, Jul 30 2015

%t Select[ Range[0, 215], PrimeQ[ FromDigits[ Flatten[ IntegerDigits /@ { #, 1, 1}]]] &] (* _Robert G. Wilson v_, Feb 21 2005 *)

%t Select[Range[0,250],PrimeQ[100#+11]&] (* _Harvey P. Dale_, Oct 11 2018 *)

%o (Magma) [n: n in [0..250] | IsPrime(Seqint(Intseq(11) cat Intseq(n)))]; // _Vincenzo Librandi_, Jul 31 2015

%o (Magma) [n: n in [0..240] |IsPrime(100*n+11)]; // _Vincenzo Librandi_, Jul 31 2015

%o (PARI) is(n)=isprime(100*n+11) \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A024912 (10n+1 is prime), A167442 (the actual primes 100n+11).

%K nonn,base

%O 1,2

%A _Parthasarathy Nambi_, Jan 30 2005, Feb 18 2005

%E Corrected and extended by _Robert G. Wilson v_, Feb 21 2005