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Numbers n such that 2*10^n+9 is prime.
1

%I #26 Jan 17 2019 13:44:06

%S 0,1,5,25,455,761,9205,13561,15955,26669,113941

%N Numbers n such that 2*10^n+9 is prime.

%C 761 and 9205 only probably prime. No others less than 10000.

%C a(12) > 2*10^5. - _Robert Price_, Jun 06 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/20009.htm#prime">Prime numbers of the form 200...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) = A101952(n-1) + 1 for n>1.

%e n = 1, 5 are members since 29 and 200009 are primes.

%t Do[ If[ PrimeQ[2*10^n + 9], Print[n]], {n, 0, 10000}]

%o (PARI) is(n)=ispseudoprime(2*10^n+9) \\ _Charles R Greathouse IV_, Jun 12 2017

%Y Cf. A081677, A088275, A101952.

%K hard,nonn

%O 1,3

%A Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

%E a(8)-a(9) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(10)-a(11) from Kamada data by _Robert Price_, Dec 13 2010

%E Prepended a(1)=0 by _Robert Price_, Jun 06 2015