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%I #38 Aug 03 2024 18:57:48
%S 3,5,35,159,237,325,355,371,481,1649,3641,4709,269623
%N Numbers k such that (10^k - 1)/3 + 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_, Apr 03 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#pwp353">Palindromic Wing Primes (PWP's)</a>
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/33533.htm#prime">Prime numbers of the form 33...33533...33</a>
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F a(n) = 2*A183175(n) + 1.
%e 5 is a term because (10^5 - 1)/3 + 2*10^2 = 33533.
%t Do[ If[ PrimeQ[(10^n + 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 4800, 2}] (* _Robert G. Wilson v_, Dec 16 2005 *)
%Y Partial sums of S(n, x), for x=1...9: A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420.
%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(13) from _Robert Price_, Aug 03 2024
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