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Numbers k such that (7*10^(2*k+1) - 9*10^k - 7)/9 is prime.
2

%I #30 Dec 06 2023 18:25:34

%S 4,5,8,11,1244,1685,2009,14657,15118,20332,50830,75062

%N Numbers k such that (7*10^(2*k+1) - 9*10^k - 7)/9 is prime.

%D C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

%H Patrick De Geest, World!Of Numbers, <a href="http://www.worldofnumbers.com/wing.htm#pwp767">Palindromic Wing Primes (PWP's)</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77677.htm#prime">Prime numbers of the form 77...77677...77</a>

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

%F a(n) = (A077788(n) - 1)/2.

%t Do[If[PrimeQ[(7*10^(2n + 1) - 9*10^n - 7)/9], Print[n]], {n, 3000}]

%o (PARI) is(n)=ispseudoprime((7*10^(2*n+1)-9*10^n-7)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

%K nonn,base

%O 1,1

%A _Ray Chandler_, Dec 28 2010

%E a(10) from _Robert Price_, Oct 07 2023

%E a(11) from _Robert Price_, Oct 17 2023

%E a(12) from _Robert Price_, Dec 06 2023