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%I #48 Oct 26 2023 11:51:01
%S 1,2,3,4,9,18,22,45,49,56,69,146,202,272,2730,2841,4562,31810,43186,
%T 48109,92691,237670
%N Numbers k such that 10^k + 9 is prime.
%C No others less than 9000. - Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
%C No others less than 39254. - Dirk Augustin, Oct 24 2006
%C 2730, 2841 and 4562 all give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005
%C Verified existing terms. No other terms less than 40001. - _Robert Price_, Aug 14 2010
%C No other terms <= 100000. - _Robert Price_, Mar 03 2011
%C a(23) > 3*10^5. - _Robert Price_, Oct 26 2023
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10009.htm#prime">Prime numbers of the form 100...009</a>.
%H Sabin Tabirca and Kieran Reynolds, <a href="http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.
%F a(n) = A102008(n) + 1.
%e 4 is a member since 10^4 + 9 = 10009 is a prime.
%t Do[ If[ PrimeQ[ 10^n + 9], Print[n]], {n, 0, 10000}] (* _Robert G. Wilson v_, Dec 16 2004 *)
%o (PARI) is(n)=isprime(10^n + 9) \\ _Charles R Greathouse IV_, Apr 29 2015
%Y Cf. A049054, A088274, A102008.
%K nonn,hard,more
%O 1,2
%A _Amarnath Murthy_, Sep 28 2003
%E a(8)-a(16) from _Ray Chandler_, Oct 10 2003
%E a(17) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005
%E a(18) (a PRP) found by Dirk Augustin, Oct 16 2006
%E a(19)-a(20) (probable primes), found with WinPFGW. No others less than 60400. - _Jason Earls_, Dec 22 2007
%E a(21) from _Robert Price_, Mar 03 2011
%E a(22) from _Robert Price_, Oct 26 2023
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