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

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, 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, 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

Offset: 0

Author

M. F. Hasler, Jan 01 2021

Keywords

• nonn
• base
• cons

Examples

			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; ...
This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.9959989998...
		

Crossrefs

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).

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

Programs

PARI

concat([digits(A098450(k))|k<-[1..14]]) \\ as seq. of digits
c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*A098450(k)) \\ as constant

Formula

c = 0.995998999899998999997999999899999997999999991999999999799999999997...

= Sum_{k >= 1} 10^(-k(k+1)/2)*A098450(k)

a(-n(n+1)/2) = 9 for all n >= 0, followed by increasingly more 9s.