A101396 - OEIS

%I #24 Sep 08 2022 08:45:16

%S 1,17,19,29,43,119,173,949,1609,5579,19679,34147,43493,97799

%N Numbers n such that 4*10^n - 9 is prime.

%C a(15) > 10^5. - _Robert Price_, Mar 17 2015

%C All terms are odd, since 4 * 10^(2*k) - 9 = (2 * 10^k - 3)*(2 * 10^k + 3). - _Robert Israel_, Mar 17 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/39991.htm#prime">Prime numbers of the form 399...991</a>.

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

%F a(n) = A101848(n) + 1.

%e n = 1, 17, 19 are members since 31, 399999999999999991 and 39999999999999999991 are primes.

%p select(n -> n::odd and isprime(4*10^n-9), [$1..10000]); # _Robert Israel_, Mar 17 2015

%t Do[ If[ PrimeQ[4*10^n - 9], Print[n]], {n, 0, 10000}]

%o (Magma) [n: n in [1..300] |IsPrime(4*10^n - 9)]; // _Vincenzo Librandi_, Mar 18 2015

%o (PARI) is(n)=ispseudoprime(4*10^n-9) \\ _Charles R Greathouse IV_, Jun 12 2017

%Y Cf. A095714, A101848.

%K more,nonn

%O 1,2

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

%E a(11) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(12)-a(14) from Kamada data by _Robert Price_, Mar 17 2015