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%I #45 Apr 20 2024 02:49:13
%S 3,4,5,9,22,27,36,57,62,78,201,537,696,790,905,1038,66886,70500,91836,
%T 100613,127240,380734,583696,719055
%N Numbers k such that 9*10^k+1 is prime.
%C a(22) > 2*10^5. - _Robert Price_, Jan 21 2015
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/90001.htm#prime">Prime numbers of the form 900...001</a>.
%H Sabin Tabirca and Kieran Reynolds, <a href="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) = A100997(n) + 1.
%e For k=9 we have (9*(10^9))+1 = 9000000001, which is prime.
%t Do[ If[ PrimeQ[9*10^n + 1], Print[n]], {n, 0, 10000}]
%o (Magma) [n: n in [0..1000] | IsPrime(9*10^n+1)]; // _Vincenzo Librandi_, May 25 2015
%o (PARI) is(n)=ispseudoprime(9*10^n+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A056806 (4*10^k+1 is prime), A100997.
%K more,nonn,changed
%O 1,1
%A _Robert G. Wilson v_, Aug 22 2005
%E a(18)-a(19) from Kamada data by _Robert Price_, Dec 14 2010
%E a(20) from _Predrag Kurtovic_, Sep 23 2013
%E a(21) from _Robert Price_, Jan 21 2015
%E a(22)-a(23) from Kamada data by _Mohammed Yaseen_, Jul 20 2021
%E a(24) from _Predrag Kurtovic_, Apr 18 2024
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