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

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, 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, 9, 7, 0, 0, 0, 2, 9, 9, 9, 9, 9, 9, 9, 9, 5

Offset

0,1

Comments

The terms of sequence A340115 converge to this sequence of digits, and to this constant, up to powers of 10.

Links

Table of n, a(n) for n=0..82.

Formula

c = 0.86472992619733697029999383759989734499700299999939482649996194672...

= Sum_{k >= 1} 10^(-k(k+1)/2)*floor(10^(k/3)-1)^3

a(-n(n+1)/2) = 9 for all n >= 3;

Example

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.
Here we list the sequence of digits of these numbers: 8; 6, 4; 7, 2, 9; 9, 2, 6, 1; ...
This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.864729926...

Prog

(PARI) concat([digits(sqrtnint(10^k-1, 3)^3)|k<-[1..14]]) \\ as seq. of digits
c(N=20)=sum(k=1, N, .1^(k*(k+1)/2)*sqrtnint(10^k-1, 3)^3) \\ as constant

Crossrefs

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).

Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).

Sequence in context: A008569 A376883 A219863 * A021906 A154187 A011329

Adjacent sequences: A340206 A340207 A340208 * A340210 A340211 A340212

Keyword

nonn,base,cons

Author

M. F. Hasler, Jan 01 2021

Status

approved