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%I #28 Apr 13 2020 01:41:45
%S 1,6,10,18,24,4978
%N Numbers n for which R(n) + 10^floor(n/2) is prime, where R(n) = (10^n-1)/9.
%C The primes corresponding to the terms of the sequence are a subset of the near-repunit primes A105992.
%C In base 10, R(n) + 10^floor(n/2) has ceiling(n/2)-1 digits 1, one digit 2, and again floor(n/2) digits 1. For odd n, this is a palindrome, for even n the digit 2 is just left to the middle of the number.
%C There cannot be an odd term > 1 since the corresponding palindrome factors as R((n+1)/2)*(10^((n-1)/2) + 1).
%C No term can be congruent to 2 mod 3. - _Chai Wah Wu_, Feb 07 2020
%H Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%e For n = 1, R(n) + 10^floor(n/2) = 2 is prime.
%e For n = 6, R(n) + 10^floor(n/2) = 112111 is prime.
%e For n = 10, R(n) + 10^floor(n/2) = 1111211111 is prime.
%o (PARI) for(n=0,9999,isprime(p=10^n\9+10^(n\2))&&print1(n","))
%Y Cf. A105992 (near-repunit primes), A002275 (repunits), A011557 (powers of 10).
%Y Cf. A331860 (variant with floor(n/2-1) instead of floor(n/2)), A331862 (variant with - (digit 0) instead of + (digit 2)).
%K nonn,more,hard,base
%O 1,2
%A _M. F. Hasler_, Jan 30 2020
%E a(6) from _Daniel Suteu_, Feb 01 2020