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Numbers k such that 9*R_(k+2) - 2*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #19 May 05 2024 19:41:41

%S 0,90,1928,2206,7244,11110,125056,131394,301354

%N Numbers k such that 9*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 98*10^k - 1 is prime.

%C Terms from Kamada.

%C a(9) > 300000.

%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/9/97999.htm#prime">Prime numbers of the form 9799...99</a>.

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

%e For k=0, 9*R_2 - 2*10^0 = 99 - 2 = 97 which is prime.

%t Select[Range[0, 300000], PrimeQ[98*10^#-1 ] &]

%o (Magma) [n: n in [0..300] | IsPrime(98*10^n-1)]; // _Vincenzo Librandi_, Apr 15 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,2

%A _Robert Price_, Apr 14 2015

%E a(9) from Kamada data by _Tyler Busby_, May 05 2024