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%I A331864 #20 Feb 03 2023 14:36:11
%S A331864 2,3,5,8,9,39,78,81,155,249,387,395,510,711,1173,1751,10245
%N A331864 Numbers k such that R(k) + 2*10^floor(k/2-1) is prime, where R(k) = (10^k-1)/9 (repunit: A002275).
%C A331864 The corresponding primes are near-repunit primes, cf. A105992.
%C A331864 In base 10, R(k) + 2*10^floor(k/2-1) has ceiling(k/2) digits 1, one digit 3 and again floor(k/2-1) digits 1: for even as well as odd k, there is a digit 3 just left of the middle of the repunit of length k.
%C A331864 No term can be equivalent to 1 (mod 3). - _Chai Wah Wu_, Feb 07 2020
%H A331864 Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%e A331864 For k = 2, R(2) + 2*10^(1-1) = 13 is prime.
%e A331864 For k = 3, R(3) + 2*10^(1-1) = 113 is prime.
%e A331864 For k = 5, R(5) + 2*10^(2-1) = 11131 is prime.
%e A331864 For k = 8, R(8) + 2*10^(4-1) = 11113111 is prime.
%o A331864 (PARI) for(n=2,999,isprime(p=10^n\9+2*10^(n\2-1))&&print1(n","))
%Y A331864 Cf. A105992 (near-repunit primes), A002275 (repunits), A011557 (powers of 10).
%Y A331864 Cf. A331865 (variant with floor(n/2) instead of floor(n/2-1)), A331860, A331863 (variants with digit 2 resp. 0 instead of digit 3).
%K A331864 nonn,base,hard,more
%O A331864 1,1
%A A331864 _M. F. Hasler_, Jan 30 2020
%E A331864 a(13)-a(16) from _Daniel Suteu_, Feb 01 2020
%E A331864 a(17) from _Michael S. Branicky_, Feb 03 2023

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