A103054 - OEIS

%I #26 Jun 03 2024 14:26:43

%S 1,3,4,7,9,13,33,37,76,147,297,1851,3457,3609,45219

%N Numbers n such that 7*10^n + 2*R_n + 7 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (65*10^n+61)/9 is prime.

%C a(16) > 10^5. - _Robert Price_, Oct 01 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/72229.htm#prime">Prime numbers of the form 722...229</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A101136(n) + 1.

%t Do[ If[ PrimeQ[(65*10^n + 61)/9], Print[n]], {n, 0, 10000}]

%t Select[Range[10000], PrimeQ[(65 10^# + 61)/9] &] (* _Vincenzo Librandi_, Oct 02 2015 *)

%o (Magma) [n: n in [0..3*10^2]| IsPrime((65*10^n+61) div 9)]; // _Vincenzo Librandi_, Oct 02 2015

%o (PARI) for(n=1, 1e4, if (isprime((65*10^n+61)/9), print1(n", "))) \\ _Altug Alkan_, Oct 02 2015

%Y Cf. A002275, A101136.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 19 2005

%E a(15) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013