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A342834 a(n) is the number whose decimal expansion consists of the concatenation of the largest 1-digit prime = 7, the largest 2-digit prime = 97, ... up to the largest n-digit prime = A003618(n).

%I A342834 #28 Jul 03 2021 05:44:52
%S A342834 7,797,797997,7979979973,797997997399991,797997997399991999983,
%T A342834 7979979973999919999839999991,797997997399991999983999999199999989,
%U A342834 797997997399991999983999999199999989999999937,7979979973999919999839999991999999899999999379999999967
%N A342834 a(n) is the number whose decimal expansion consists of the concatenation of the largest 1-digit prime = 7, the largest 2-digit prime = 97, ... up to the largest n-digit prime = A003618(n).
%C A342834 a(n) has n*(n+1)/2 digits.
%C A342834 a(1) = 7 and a(2) = 797, these are only 2 known indices for which a(n) = A338968(n).
%C A342834 The decimal expansion of the limit when n -> oo of a(n) is A340220.
%e A342834 The greatest primes with 1, 2 and 3 digits are respectively 7, 97 and 997, hence, a(3) = 7||97||997 = 797997 where || stands for concatenation.
%o A342834 (Python)
%o A342834 from sympy import prevprime
%o A342834 def aupton(nn):
%o A342834   astr, alst = "", []
%o A342834   for n in range(1, nn+1):
%o A342834     astr += str(prevprime(10**n)); alst.append(int(astr))
%o A342834   return alst
%o A342834 print(aupton(10)) # _Michael S. Branicky_, Mar 23 2021
%o A342834 (PARI) a(n) = my(s=""); for (k=1, n, s = Str(s, precprime(10^k))); eval(s); \\ _Michel Marcus_, Mar 24 2021
%Y A342834 Cf. A000217 (number of digits), A338968, A340220, A342835 (number of divisors), A342836 (smallest prime factor).
%K A342834 nonn,base
%O A342834 1,1
%A A342834 _Bernard Schott_, Mar 23 2021