A257031 - OEIS

%I #26 Apr 20 2024 02:48:00

%S 1,2,5,10,11,16,23,247,1700,2891,3019,5549,5837,9326,14417,23312,

%T 24155,30740,61907,64421,69997,78656,163106,177266

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

%C Also, numbers k such that (682*10^k - 7)/9 is prime.

%C Terms from Kamada.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abaaa.htm">Near-repdigit numbers of the form ABAA...AA</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/75777.htm#prime">Prime numbers of the form 7577...77</a>.

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

%e For k=5, 7*R_7 - 2*10^5 = 7777777 - 200000 = 7577777 which is prime.

%t Select[Range[0, 30000], PrimeQ[(682*10^#-7)/9 ] &]

%o (Magma) [n: n in [0..400] | IsPrime((682*10^n-7) div 9)]; // _Vincenzo Librandi_, Apr 15 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,2

%A _Robert Price_, Apr 14 2015

%E a(18)-a(24) from Kamada data by _Tyler Busby_, Apr 16 2024