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%I #21 Aug 03 2017 05:00:53
%S 0,1,11111111111,
%T 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
%N Double repunit numbers: repunits with repunit indices.
%C a(3) has 111 digits.
%C 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 Are there any primes in this sequence? In other words, is there a term of A004022 that is also a term of A004023?
%C 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 a(n) = A002275(A002275(n)).
%t Table[Nest[FromDigits@ ConstantArray[1, #] &, n, 2], {n, 0, 3}] (* _Michael De Vlieger_, Jul 30 2017 *)
%o (PARI) a002275(n) = (10^n-1)/9
%o a(n) = a002275(a002275(n))
%Y Cf. A002275, A004022, A004023, A077585.
%K nonn,base,easy,bref
%O 0,3
%A _Felix Fröhlich_, Jul 29 2017
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