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Numbers n such that 5*10^n + 6*R_n + 3 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
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%I #23 Jul 13 2023 12:26:49

%S 1,2,3,10,25,29,34,73,76,77,651,884,938,1252,1893,3342,4034,6168,6216,

%T 6231,6812,11046,15448,16628,16918,18734,45935,130393,139289,158819

%N Numbers n such that 5*10^n + 6*R_n + 3 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (17*10^n+7)/3 is prime.

%C a(31) > 3*10^5. - _Robert Price_, Jul 13 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/56669.htm#prime">Prime numbers of the form 566...669</a>.

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

%F a(n) = A101583(n) + 1.

%t Do[ If[ PrimeQ[(17*10^n + 7)/3], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101583.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 18 2005

%E a(22)-a(26) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(27) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013

%E a(28)-a(30) from _Robert Price_, Jul 13 2023