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Numbers n such that n concatenated with n 1's is a prime.
9

%I #31 Jun 28 2018 03:08:15

%S 1,2,5,7,10,16,20,65,91,119,169,290,428,610,905,1051,3488,4526,6445,

%T 8693,32059

%N Numbers n such that n concatenated with n 1's is a prime.

%C There is no further term up to 10000. - _Farideh Firoozbakht_, Sep 23 2009

%C No more terms through 20000. - _Jon E. Schoenfield_, Mar 24 2018

%C a(22) > 50000, if it exists. - _Giovanni Resta_, Jun 28 2018

%D Jason Earls, On Smarandache Repunit N Numbers, Smarandache Notions Journal (2004), Vol. 14.1, pp. 251-258.

%e 5 is a member as 5 followed by five 1's, 511111, is a prime.

%t Do[ If[ PrimeQ[ FromDigits[ Join[IntegerDigits[n], IntegerDigits[(10^n - 1)/9]]]], Print[n]], {n, 1, 1700}]

%o (PARI) for(n=1,520, if(isprime(n*10^n+(10^n-1)/9)==1,print1(n,",")))

%Y Cf. A070220, A070746.

%K nonn,base,more

%O 1,2

%A _Amarnath Murthy_, Mar 07 2002

%E More terms from _Benoit Cloitre_, Mar 09 2002

%E Further terms from _Vladeta Jovovic_, _Amarnath Murthy_ and _Robert G. Wilson v_, May 03 2002

%E a(17) (a probable prime) from _Rick L. Shepherd_, May 10 2002

%E a(18)-a(19) (probable primes) from _Jason Earls_, Oct 15 2002

%E a(20) from _Farideh Firoozbakht_, Sep 23 2009

%E a(21) from _Giovanni Resta_, Jun 28 2018