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%I #40 Sep 05 2023 13:33:14
%S 0,1,7,45,115,681,1248,2481,2689,6198,13197,60126,100072
%N Numbers n such that (10^(2n+1) + 36*10^n - 1)/9 is prime.
%C n is in the sequence iff the palindromic number 1(n).5.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+2, 18m+12, 18m+14, 22m+4, 22m+6, etc. (the proof is easy).
%C a(14) > 100233. - __Robert Price_, Sep 05 2023
%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#pwp151">Palindromic Wing Primes (PWP's)</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11511.htm#prime">Prime numbers of the form 11...11511...11</a>
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = (A077783(n)-1)/2.
%e 1248 is in the sequence because (10^(2*1248+1)+36*10^1248-1)/9=1(1248).5.1(1248) is prime.
%t Do[If[PrimeQ[(10^(2n + 1) + 36*10^n - 1)/9], Print[n]], {n, 2200}]
%o (Magma) [n: n in [0..700] | IsPrime((10^(2*n+1)+36*10^n-1) div 9)]; // _Vincenzo Librandi_, Oct 13 2015
%o (PARI) is(n)=ispseudoprime((10^(2*n+1)+36*10^n-1)/9) \\ _Charles R Greathouse IV_, Jun 06 2017
%Y Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.
%K nonn,base,more
%O 1,3
%A _Farideh Firoozbakht_, May 19 2005
%E Edited by _Ray Chandler_, Dec 28 2010
%E a(12) from _Robert Price_, Oct 12 2015
%E a(13) from _Robert Price_, Sep 05 2023
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