cp's OEIS Frontend

A340220 Constant whose decimal expansion is the concatenation of the largest n-digit prime A003618(n), for n = 1, 2, 3, ...

%I A340220 #5 May 06 2022 13:13:51
%S A340220 7,9,7,9,9,7,9,9,7,3,9,9,9,9,1,9,9,9,9,8,3,9,9,9,9,9,9,1,9,9,9,9,9,9,
%T A340220 8,9,9,9,9,9,9,9,9,3,7,9,9,9,9,9,9,9,9,6,7,9,9,9,9,9,9,9,9,9,7,7,9,9,
%U A340220 9,9,9,9,9,9,9,9,8,9,9,9,9,9,9,9,9,9,9,9,9,7,1
%N A340220 Constant whose decimal expansion is the concatenation of the largest n-digit prime A003618(n), for n = 1, 2, 3, ...
%C A340220 This is the limit of the terms of A338968, either digit-wise, or as a constant, up to powers of 10.
%F A340220 c = 0.797997997399991999983999999199999989999999937999999996799999999977...
%F A340220   = Sum_{k >= 1} 10^(-k(k+1)/2)*A003618(k)
%F A340220 a(-n(n+1)/2) = 9 for all n >= 0, followed by increasingly more 9s.
%e A340220 The smallest prime with 1, 2, 3, 4, ... digits is, respectively, 7, 97, 997, 9973, 99991, 999983, ...
%e A340220 Here we list the sequence of digits of these numbers: 7; 9, 7; 9, 9, 7; 9, 9, 7, 3; ...
%e A340220 This can be considered, as for the Champernowne and Copeland-Erdős constants, as the decimal expansion of a real constant 0.797997997399991...
%o A340220 (PARI) concat([digits(precprime(10^k))|k<-[1..14]]) \\ as seq. of digits
%o A340220 c(N=20)=sum(k=1,N,.1^(k*(k+1)/2)*precprime(10^k)) \\ as constant
%Y A340220 Cf. A003618 (largest n-digit prime), A340222 (same with semiprimes), A340207 (same for squares, limit of A339978), A340209 (same for cubes, limit of A340115), A340219 (similar for smallest n-digit primes, limit of A215641), A340221 (similar, with smallest semiprime, limit of A215647), A340206 (similar, with smallest n-digit squares, limit of A215689), A340208 (similar, with smallest n-digit cubes, limit of A215692), A340220 (same for primes, limit of A338968).
%Y A340220 Cf. A033307 (Champernowne constant), A030190 (binary), A001191 (concatenation of all squares), A134724 (cubes), A033308 (primes: Copeland-Erdős constant).
%K A340220 nonn,base,cons
%O A340220 0,1
%A A340220 _M. F. Hasler_, Jan 01 2021