%I #45 Mar 26 2020 06:16:23
%S 3,7,15,21,25,961,1899,3891,15097,17847
%N Numbers k such that 7*(10^k - 1)/9 - 5*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(11) > 2*10^5. - _Robert Price_, Nov 02 2015
%C A183178(1) = 0 would correspond to an initial term 1 in this sequence which yields the prime 2 (which has a "wing" of length 0 and is a palindrome and repdigit but not near-repdigit). - _M. F. Hasler_, Feb 08 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#pwp727">Palindromic Wing Primes (PWP's)</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77277.htm#prime">Prime numbers of the form 77...77277...77</a>
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = 2*A183178(n+1) + 1.
%e 15 is a term because 7*(10^15 - 1)/9 - 5*10^7 = 777777727777777.
%t Do[ If[ PrimeQ[(7*10^n - 45*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 1000, 2}] (* _Robert G. Wilson v_, Dec 16 2005 *)
%o (PARI) for(k=1,oo,ispseudoprime(10^k\9*7-5*10^(k\2))&&print1(k",")) \\ _M. F. Hasler_, Feb 08 2020
%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