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%I #42 Mar 26 2020 11:13:49
%S 3,5,39,195,19637
%N Numbers k such that (10^k - 1)/9 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).
%C Prime versus probable prime status and proofs are given in the author's table.
%C a(6) > 2*10^5. - _Robert Price_, Apr 02 2016
%C The number k = 1 would also correspond to a prime, 3, but not "near-repdigit" or "wing" in a strict sense. - _M. F. Hasler_, Feb 09 2020
%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#pwp131">Palindromic Wing Primes (PWP's)</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11311.htm#prime">Prime numbers of the form 11...11311...11</a>
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = 2*A107123(n+1) + 1.
%e 5 is a term because (10^5 - 1)/9 + 2*10^2 = 11311.
%t Do[ If[ PrimeQ[(10^n + 18*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 20000, 2}] (* _Robert G. Wilson v_, Dec 16 2005 *)
%Y Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.
%Y See A332113 for the (prime and composite) near-repunit palindromes 1..131..1.
%K nonn,base,more
%O 1,1
%A _Patrick De Geest_, Nov 16 2002
%E Name corrected by _Jon E. Schoenfield_, Oct 31 2018
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