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 A290390 #21 Aug 03 2017 05:00:53
%S A290390 0,1,11111111111,
%T A290390 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
%N A290390 Double repunit numbers: repunits with repunit indices.
%C A290390 a(3) has 111 digits.
%C A290390 As in the case of A077585, where a necessary condition for a term to be prime is that its index is a Mersenne prime, a necessary (but not sufficient) condition for a term of this sequence to be prime is that the number of ones is a repunit prime, i.e., A055642(a(n)) must be a term of A004022.
%C A290390 Are there any primes in this sequence? In other words, is there a term of A004022 that is also a term of A004023?
%C A290390 Second sequence in the hierarchy of sequences obtained by successive numbers of nestings of the form A002275(...A002275(n)...). All higher order sequences in this hierarchy grow much too fast to be included in the OEIS.
%F A290390 a(n) = A002275(A002275(n)).
%t A290390 Table[Nest[FromDigits@ ConstantArray[1, #] &, n, 2], {n, 0, 3}] (* _Michael De Vlieger_, Jul 30 2017 *)
%o A290390 (PARI) a002275(n) = (10^n-1)/9
%o A290390 a(n) = a002275(a002275(n))
%Y A290390 Cf. A002275, A004022, A004023, A077585.
%K A290390 nonn,base,easy,bref
%O A290390 0,3
%A A290390 _Felix Fröhlich_, Jul 29 2017