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A338968 a(n) is the largest prime whose decimal expansion consists of the concatenation of a 1-digit prime, a 2-digit prime, a 3-digit prime, ..., and an n-digit prime.

%I A338968 #66 Mar 25 2021 12:42:13
%S A338968 7,797,797977,7979979941,797997997399817,797997997399991999371,
%T A338968 7979979973999919999839999901,797997997399991999983999999199999131,
%U A338968 797997997399991999983999999199999989999997639,7979979973999919999839999991999999899999999379999997871
%N A338968 a(n) is the largest prime whose decimal expansion consists of the concatenation of a 1-digit prime, a 2-digit prime, a 3-digit prime, ..., and an n-digit prime.
%C A338968 It is a plausible conjecture that a(n) always exists and begins with 7.
%C A338968 The similar smallest primes are in A215641.
%C A338968 If a(n) exists, it has A000217(n) = n*(n+1)/2 digits.
%C A338968 a(1) = 7 = A003618(1) and a(2) = 797 is the concatenation of 7 = A003618(1) and 97 = A003618(2)  that are respectively the largest 1-digit prime and 2-digit prime.
%C A338968 Conjecture: for n >= 3, a(n) is the concatenation of the largest k-digit primes with 1 <= k <= n-1: A003618(1)/A003618(2)/.../A003618(n-1) but the last concatenated prime with n digits is always < A003618(n). This conjecture has been checked by _Daniel Suteu_ until a(360), a prime with 64980 digits.
%e A338968 a(3) = 797977 is the largest prime formed from the concatenation of a single-digit, a double-digit, a triple-digit prime, i.e., 7, 97, 977.
%e A338968 a(4) = 7979979941 is the largest prime formed from the concatenation of a single-digit, a double-digit, a triple-digit, and a quadruple-digit prime, i.e., 7, 97, 997, 9941.
%Y A338968 Cf. A000217, A003618, A215641.
%Y A338968 Subsequence of A195302.
%Y A338968 Cf. A339978 (with concatenated squares), A340115 (with concatenated cubes).
%K A338968 nonn,base
%O A338968 1,1
%A A338968 _Bernard Schott_, Dec 21 2020
%E A338968 More terms from _David A. Corneth_, Dec 21 2020