

A340207


Constant whose decimal expansion is the concatenation of the largest ndigit square A061433(n), for n = 1, 2, 3, ...


6



9, 8, 1, 9, 6, 1, 9, 8, 0, 1, 9, 9, 8, 5, 6, 9, 9, 8, 0, 0, 1, 9, 9, 9, 8, 2, 4, 4, 9, 9, 9, 8, 0, 0, 0, 1, 9, 9, 9, 9, 5, 0, 8, 8, 4, 9, 9, 9, 9, 8, 0, 0, 0, 0, 1, 9, 9, 9, 9, 9, 5, 1, 5, 5, 2, 9, 9, 9, 9, 9, 9, 8, 0, 0, 0, 0, 0, 1, 9, 9, 9, 9, 9, 9, 5, 8
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OFFSET

0,1


COMMENTS

The terms of sequence A339978 converge to this sequence of digits, and to this constant, up to powers of 10.


LINKS

Table of n, a(n) for n=0..85.


FORMULA

c = 0.9819619801998569980019998244999800019999508849999800001999995155...
= Sum_{k >= 1} 10^(k(k+1)/2)*floor(10^(k/2)1)^2
a(n(n+1)/2) = 9 for all n >= 2.


EXAMPLE

The largest square with 1, 2, 3, 4, ... digits is, respectively, 9 = 3^2, 81 = 9^2, 961 = 31^2, 9801 = 99^2, ....
Here we list the sequence of digits of these numbers: 9; 8, 1; 9, 6, 1; 9, 8, 0, 1; 9, 9, 8, 5, 6; ...
This can be considered, as for the Champernowne and CopelandErdős constants, as the decimal expansion of a real constant 0.98196198...


PROG

(PARI) concat([digits(sqrtint(10^k1)^2)k<[1..14]]) \\ as seq. of digits
c(N=20)=sum(k=1, N, .1^(k*(k+1)/2)*sqrtint(10^k1)^2) \\ as constant


CROSSREFS

Cf. A061433 (largest ndigit square), A339978 (has this as "limit"), A340208 (same with "smallest ndigit cube", limit of A215692), A340209 (same for cubes, limit of A340115), A340220 (same for primes), A340219 (similar with smallest primes, limit of A215641), A340222 (same for semiprimes), A340221 (same for smallest semiprimes, limit of A215647).
Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: CopelandErdős constant).
Sequence in context: A244978 A114864 A261025 * A185260 A275615 A249677
Adjacent sequences: A340204 A340205 A340206 * A340208 A340209 A340210


KEYWORD

nonn,base,cons


AUTHOR

M. F. Hasler, Jan 01 2021


STATUS

approved



