A056718 - OEIS

%I #27 Feb 28 2020 21:25:18

%S 1,2,4,10,13,25,115,179,181,238,785,799,1193,1730,1811,1871,2116,2180,

%T 17878,22093,30976,31631,43271,52763,66575

%N Numbers k such that (61*10^k - 7)/9 is prime.

%C Or, numbers k such that 6*10^k + 7*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/6/67777.htm#prime">Prime numbers of the form 677...77</a>.

%H Maksym Voznyy, <a href="http://max0526.fcpages.com/2116.zip">Primo certificate for 2116</a>

%H Maksym Voznyy, <a href="http://max0526.fcpages.com/2180.zip">Primo certificate for 2180</a>

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

%t Do[ If[ PrimeQ[ 6*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 5000}]

%o (PARI) is(n)=ispseudoprime((61*10^n-7)/9) \\ _Charles R Greathouse IV_, Jun 12 2017

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 11 2000

%E The PRP's corresponding to 2116 and 2180 have been proved to be prime by Maksym Voznyy (mvoznyy0526(AT)rogers.com), Jan 05 2008, who has found 2 new PRP's, which correspond to 17878 and 22093

%E Definition corrected by _N. J. A. Sloane_, Jan 05 2008

%E 30976, 31631 and 43271 from Maksym Voznyy, Jan 2008 confirmed as next terms of sequence by _Ray Chandler_, Feb 06 2012

%E 52763 from Serge Batalov, Feb 27 2009 confirmed as next term of sequence by _Ray Chandler_, Feb 06 2012

%E 66575 from _Ray Chandler_, Feb 06 2012