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Numbers k such that (10^(2k+1) + 6*10^k - 1)/3 is prime.
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%I #27 Aug 03 2024 18:58:06

%S 1,2,17,79,118,162,177,185,240,824,1820,2354,134811

%N Numbers k such that (10^(2k+1) + 6*10^k - 1)/3 is prime.

%C a(13) > 10^5. - _Robert Price_, Apr 03 2016

%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#pwp353">Palindromic Wing Primes (PWP's)</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/33533.htm#prime">Prime numbers of the form 33...33533...33</a>.

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

%F a(n) = (A077784(n) - 1)/2.

%t Do[If[PrimeQ[(10^(2n + 1) + 6*10^n - 1)/3], Print[n]], {n, 3000}]

%o (PARI) is(n)=ispseudoprime((10^(2*n+1)+6*10^n-1)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,base

%O 1,2

%A _Ray Chandler_, Dec 28 2010

%E a(13) from _Robert Price_, Aug 03 2024