This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331861 #28 Apr 13 2020 01:41:45 %S A331861 1,6,10,18,24,4978 %N A331861 Numbers n for which R(n) + 10^floor(n/2) is prime, where R(n) = (10^n-1)/9. %C A331861 The primes corresponding to the terms of the sequence are a subset of the near-repunit primes A105992. %C A331861 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 A331861 There cannot be an odd term > 1 since the corresponding palindrome factors as R((n+1)/2)*(10^((n-1)/2) + 1). %C A331861 No term can be congruent to 2 mod 3. - _Chai Wah Wu_, Feb 07 2020 %H A331861 Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015). %e A331861 For n = 1, R(n) + 10^floor(n/2) = 2 is prime. %e A331861 For n = 6, R(n) + 10^floor(n/2) = 112111 is prime. %e A331861 For n = 10, R(n) + 10^floor(n/2) = 1111211111 is prime. %o A331861 (PARI) for(n=0,9999,isprime(p=10^n\9+10^(n\2))&&print1(n",")) %Y A331861 Cf. A105992 (near-repunit primes), A002275 (repunits), A011557 (powers of 10). %Y A331861 Cf. A331860 (variant with floor(n/2-1) instead of floor(n/2)), A331862 (variant with - (digit 0) instead of + (digit 2)). %K A331861 nonn,more,hard,base %O A331861 1,2 %A A331861 _M. F. Hasler_, Jan 30 2020 %E A331861 a(6) from _Daniel Suteu_, Feb 01 2020