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%I #37 Jul 10 2023 10:27:11
%S 1,2,4,6,11,12,13,35,46,57,128,156,263,353,396,429,783,982,1058,1563,
%T 1695,1816,1937,4236,4431,6858,9898,13145,16646,20891,63351,105296,
%U 113693,121144,163780,234915,284751
%N Numbers k such that 7*10^k + 9 is prime.
%C a(38) > 3*10^5. - _Robert Price_, Jul 10 2023
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/70009.htm#prime">Prime numbers of the form 700...009</a>.
%H Sabin Tabirca and Kieran Reynolds, <a href="https://web.archive.org/web/20220421133441/http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = A101130(n) + 1.
%e k=2 we get 7*10^2+9 = 7*100+9 = 709, which is prime.
%t Do[ If[ PrimeQ[ 7*10^n + 9], Print[ n ]], {n, 0, 10000}] (* _Robert G. Wilson v_, Jan 19 2005 *)
%t Select[Range[0, 10000], PrimeQ[7 10^# + 9] &] (* _Vincenzo Librandi_, Sep 06 2015 *)
%o (Magma) [n: n in [0..400] |IsPrime(7*10^n + 9)]; // _Vincenzo Librandi_, Sep 06 2015
%o (PARI) is(n)=ispseudoprime(7*10^n+9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A101130.
%K more,nonn
%O 1,2
%A Julien Peter Benney (jpbenney(AT)ftml.net), Sep 05 2004
%E a(19)-a(27) from _Robert G. Wilson v_, Jan 19 2005
%E a(28)-a(31) from Kamada data by _Robert Price_, Dec 14 2010
%E a(32)-a(35) from _Robert Price_, Sep 05 2015
%E a(36)-a(37) from _Robert Price_, Jul 10 2023
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