login
Numbers n such that 4*10^n + 5*R_n + 2 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
3

%I #22 Jan 17 2019 13:44:07

%S 1,2,4,5,13,22,25,28,38,67,142,284,295,380,397,1217,1640,2885,3286,

%T 7735,29306

%N Numbers n such that 4*10^n + 5*R_n + 2 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (41*10^n+13)/9 is prime.

%C a(22) > 10^5. - _Robert Price_, May 22 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/45557.htm#prime">Prime numbers of the form 455...557</a>.

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

%F a(n) = A101727(n) + 1.

%t Do[ If[ PrimeQ[(41*10^n + 13)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101727.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 17 2005

%E Addition of a(21) from Kamada data by _Robert Price_, Dec 09 2010