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A340222 Constant whose decimal expansion is the concatenation of the largest n-digit semiprime A098450(n), for n = 1, 2, 3, ...

%I A340222 #5 May 06 2022 13:13:51
%S A340222 9,9,5,9,9,8,9,9,9,8,9,9,9,9,8,9,9,9,9,9,7,9,9,9,9,9,9,8,9,9,9,9,9,9,
%T A340222 9,7,9,9,9,9,9,9,9,9,1,9,9,9,9,9,9,9,9,9,7,9,9,9,9,9,9,9,9,9,9,7,9,9,
%U A340222 9,9,9,9,9,9,9,9,9,7,9,9,9,9,9,9,9,9,9,9,9,8,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A340222 Constant whose decimal expansion is the concatenation of the largest n-digit semiprime A098450(n), for n = 1, 2, 3, ...
%F A340222 c = 0.995998999899998999997999999899999997999999991999999999799999999997...
%F A340222   = Sum_{k >= 1} 10^(-k(k+1)/2)*A098450(k)
%F A340222 a(-n(n+1)/2) = 9 for all n >= 0, followed by increasingly more 9s.
%e A340222 The smallest prime with 1, 2, 3, 4, ... digits is, respectively, 9 = 3^2, 95 = 5*19, 998 = 2*499, 9998 = 2*4999, .... Here we list the sequence of digits of these numbers: 9: 9, 5; 9, 9, 8; 9, 9, 9, 8; ...
%e A340222 This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.9959989998...
%o A340222 (PARI) concat([digits(A098450(k))|k<-[1..14]]) \\ as seq. of digits
%o A340222 c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*A098450(k)) \\ as constant
%Y A340222 Cf. A098450 (largest n-digit semiprime), A340221 (similar, with smallest semiprime, limit of A215647), A340207 (same for squares, limit of A339978), A340206 (similar, with smallest n-digit squares, limit of A215689), A340209 (same with cubes, limit of A340115), A340208 (similar, with smallest n-digit cubes, limit of A215692), A340220 (same for primes, limit of A338968), A340219 (similar for smallest n-digit primes, limit of A215641).
%Y A340222 Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).
%K A340222 nonn,base,cons
%O A340222 0,1
%A A340222 _M. F. Hasler_, Jan 01 2021