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%I #32 Jan 17 2019 13:44:08
%S 0,3,33,311,2933,22235,39165,41585
%N Numbers n such that (10^(2n+1)+54*10^n-1)/9 is prime.
%C n is in the sequence iff the palindromic number 1(n).7.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 6m, 6m+2, 7m+2, 16m+9, 16m+14, 18m+1, 18m+7, 22m+13, 22m+19, etc. (the proof is easy).
%C a(9) > 10^5. - _Robert Price_, Apr 30 2017
%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#pwp171">Palindromic Wing Primes (PWP's)</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11711.htm#prime">Prime numbers of the form 11...11711...11</a>
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = (A077789(n)-1)/2.
%e 3 is in the sequence because (10^(2*3+1)+54*10^3-1)/9=1(3).7.1(3)=1117111 is prime.
%e 2933 is in the sequence because (10^(2*2933+1)+54*10^2933-1)/9=1(2933).7.1(2933) is prime.
%t Do[If[PrimeQ[(10^(2n + 1) + 54*10^n - 1)/9], Print[n]], {n, 3250}]
%o (PARI) for(n=0,1e4,if(ispseudoprime(t=(10^(2*n+1)+54*10^n)\9),print1(t", "))) \\ _Charles R Greathouse IV_, Jul 15 2011
%Y Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.
%K nonn,more,base
%O 1,2
%A _Farideh Firoozbakht_, May 19 2005
%E Edited by _Ray Chandler_, Dec 28 2010
%E a(6)-a(8) from _Robert Price_, Apr 30 2017
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