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Numbers k such that 7*(10^k - 1)/9 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).
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%I #35 Mar 26 2020 11:13:17

%S 3,5,17,39,41,425,561,1775,2043,11031,16233,23705

%N Numbers k such that 7*(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(13) > 2*10^5. - _Robert Price_, Jan 19 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#pwp797">Palindromic Wing Primes (PWP's)</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77977.htm#prime">Prime numbers of the form 77...77977...77</a>

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

%F a(n) = 2*A183183(n) + 1.

%e 17 is a term because 7*(10^17 - 1)/9 + 2*10^8 = 77777777977777777.

%t Do[ If[ PrimeQ[(7*10^n + 18*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 23800, 2}] (* _Robert G. Wilson v_, Dec 16 2005 *)

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

%K more,nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 16 2002

%E Name corrected by _Jon E. Schoenfield_, Oct 31 2018