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Numbers n such that 5*10^n + 4*R_n - 3 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
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%I #16 Jan 17 2019 13:44:07

%S 0,2,3,86,134,185,344,396,476,834,1799,2147,2418,5216,5882,6216,13394,

%T 19746,66485

%N Numbers n such that 5*10^n + 4*R_n - 3 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (49*10^n-31)/9 is prime.

%C a(20) > 10^5. - _Robert Price_, Jul 16 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/54441.htm#prime">Prime numbers of the form 544...441</a>.

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

%F a(n) = A101578(n-1) + 1, for n>1.

%t Do[ If[ PrimeQ[(49*10^n - 31)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101578.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 18 2005

%E a(17)-a(18) from Kamada data by _Robert Price_, Dec 14 2010

%E a(1) = 0 prepended by _Robert Price_, Jul 16 2015

%E a(19) from _Robert Price_, Jul 16 2015