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A056714 Numbers n such that 5*10^n + 3*R_n is prime, where R_n = 11...1 is the repunit (A002275) of length n. 1


%S 0,1,3,13,25,49,143,419,1705,13993,35753,40889

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

%C Also numbers n such that (16*10^n-1)/3 is prime.

%C 5*10^a(n)+3*(10^a(n)-1)/9 is a solution for part (b) of questions of puzzle 244 from www.primepuzzles.net. If a(n) is greater than 5812 then a(n) is an example that is asked for in this question. - _Farideh Firoozbakht_, Dec 02 2003

%H Makoto Kamada, <a href="http://stdkmd.com/nrr/5/53333.htm#prime">Prime numbers of the form 533...33</a>.

%H Prime Puzzles, <a href="http://www.primepuzzles.net/puzzles/puzz_244.htm">Puzzle 244</a>

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

%t Do[ If[ PrimeQ[ 5*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]

%Y Cf. A002275, A093674.

%K nonn

%O 1,3

%A _Robert G. Wilson v_, Aug 11 2000

%E 1705 from _Farideh Firoozbakht_, Dec 18 2003

%E 13993, 35753 and 40889 from Serge Batalov, Jan 2009 confirmed as next terms by _Ray Chandler_, Feb 11 2012

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Last modified August 28 10:50 EDT 2015. Contains 261120 sequences.