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Numbers k such that (10^k - 1)/9 + 7*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).
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%I #30 Aug 03 2024 18:59:11

%S 3,9,13,15,769,1333,1351,6331,262041

%N Numbers k such that (10^k - 1)/9 + 7*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.

%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#pwp181">Palindromic Wing Primes (PWP's)</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11811.htm#prime">Prime numbers of the form 11...11811...11</a>

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

%F a(n) = 2*A107648(n) + 1.

%e 13 is a term (10^13 - 1)/9 + 7*10^6 = 1111118111111.

%t Do[ If[ PrimeQ[(10^n + 63*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 6400, 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

%E a(9) from _Robert Price_, Aug 03 2024