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A340221 Constant whose decimal expansion is the concatenation of the smallest n-digit semiprime A098449(n), for n = 1, 2, 3, ...

%I A340221 #6 May 06 2022 13:13:51
%S A340221 4,1,0,1,0,6,1,0,0,3,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,
%T A340221 0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,6,1,0,0,0,0,0,0,0,0,0,3,1,0,
%U A340221 0,0,0,0,0,0,0,0,0,7,1,0,0,0,0,0,0,0,0,0,0,0,7,1,0,0,0,0,0,0,0,0,0,0,0
%N A340221 Constant whose decimal expansion is the concatenation of the smallest n-digit semiprime A098449(n), for n = 1, 2, 3, ...
%C A340221 The terms of sequence A215647 converge to this sequence of digits, and to this constant, up to powers of 10.
%F A340221 c = 0.410106100310001100001100000110000001100000001100000000610000000003...
%F A340221   = Sum_{k >= 1} 10^(-k(k+1)/2)*A098449(k)
%F A340221 a(-n(n+1)/2) = 1 for all n >= 2, followed by increasingly more zeros.
%e A340221 The smallest prime with 1, 2, 3, 4, ... digits is, respectively, 2, 11, 101, 1009, .... Here we list the sequence of digits of these numbers: 2: 1, 1; 1, 0, 1; 1, 0, 0, 9; ...
%e A340221 This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.2111011009...
%o A340221 (PARI) concat([digits(A098449(k))|k<-[1..14]]) \\ as seq. of digits
%o A340221 c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*A098449(k)) \\ as constant
%Y A340221 Cf. A098449 (smallest n-digit semiprime), A215647 (has this as "limit"), A340206 (same for squares, limit of A215689), A340207 (similar, with largest n-digit squares, limit of A339978), A340208 (same for cubes, limit of A215692), A340209 (same with largest n-digit cube, limit of A340115), A340219 (same for primes, limit of A215641).
%Y A340221 Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).
%K A340221 nonn,base,cons
%O A340221 0,1
%A A340221 _M. F. Hasler_, Jan 01 2021