cp's OEIS Frontend

A340209 Constant whose decimal expansion is the concatenation of the largest n-digit cube A061435(n), for n = 1, 2, 3, ...

%I A340209 #6 May 06 2022 13:13:51
%S A340209 8,6,4,7,2,9,9,2,6,1,9,7,3,3,6,9,7,0,2,9,9,9,9,3,8,3,7,5,9,9,8,9,7,3,
%T A340209 4,4,9,9,7,0,0,2,9,9,9,9,9,9,3,9,4,8,2,6,4,9,9,9,6,1,9,4,6,7,2,1,9,9,
%U A340209 9,7,0,0,0,2,9,9,9,9,9,9,9,9,5
%N A340209 Constant whose decimal expansion is the concatenation of the largest n-digit cube A061435(n), for n = 1, 2, 3, ...
%C A340209 The terms of sequence A340115 converge to this sequence of digits, and to this constant, up to powers of 10.
%F A340209 c = 0.86472992619733697029999383759989734499700299999939482649996194672...
%F A340209   = Sum_{k >= 1} 10^(-k(k+1)/2)*floor(10^(k/3)-1)^3
%F A340209 a(-n(n+1)/2) = 9 for all n >= 3;
%e A340209 The largest cube with 1, 2, 3, 4, ... digits is, respectively, 8 = 2^3, 64 = 4^3, 729 = 9^3, 9261 = 21^3, ..., cf. A061435.
%e A340209 Here we list the sequence of digits of these numbers: 8; 6, 4; 7, 2, 9; 9, 2, 6, 1; ...
%e A340209 This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.864729926...
%o A340209 (PARI) concat([digits(sqrtnint(10^k-1,3)^3)|k<-[1..14]]) \\ as seq. of digits
%o A340209 c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*sqrtnint(10^k-1,3)^3) \\ as constant
%Y A340209 Cf. A061435 (largest n-digit cube), A340115 (has this as "limit"), A340208 (similar, with smallest n-digit cubes, limit of A215692), A340207 (same for squares, limit of A339978), A340220 (same for primes), A340222 (same for semiprimes), A340219 (similar, with smallest primes, limit of A215641), A340221 (similar, with smallest semiprimes, limit of A215647).
%Y A340209 Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).
%K A340209 nonn,base,cons
%O A340209 0,1
%A A340209 _M. F. Hasler_, Jan 01 2021