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A030168 Continued fraction for Copeland-Erdős constant 0.235711... (concatenate primes).

%I A030168 #27 Feb 16 2025 08:32:35
%S A030168 0,4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,4,2,2,1,1,2,1,4,39,4,4,5,
%T A030168 2,1,1,87,16,1,2,1,2,1,1,3,1,8,1,3,1,1,6,1,13,27,1,1,3,1,41,1,2,1,1,
%U A030168 19,1,1,1,1,3,1,1,484,1,4,1,19,3,6,8,1,5,1,17,9,2,3,5,25,1468,1,1,3,1
%N A030168 Continued fraction for Copeland-Erdős constant 0.235711... (concatenate primes).
%H A030168 M. F. Hasler, <a href="/A030168/b030168.txt">Table of n, a(n) for n = 0..5000</a>
%H A030168 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A030168 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Copeland-ErdosConstant.html">Copeland-Erdős Constant</a>
%H A030168 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A030168 0.23571113171923293137414347... = 0 + 1/(4 + 1/(4 + 1/(8 + 1/(16 + ...))))
%t A030168 Take[ ContinuedFraction@ FromDigits[{Flatten[ IntegerDigits[ Prime@Range@ 47]], 0}], 95] (* _Robert G. Wilson v_, Oct 17 2013 *)
%o A030168 (PARI)
%o A030168 s=concat(vector(2000,i,Str(prime(i)))); c=contfrac(eval(s)/10^#s);
%o A030168 c2=contfrac((eval(s)+10^9)/10^#s);
%o A030168 for(i=1,#c, c[i]!=c2[i] & return(Str("Terms may be wrong for n>="i-1));
%o A030168 write("b030168.txt",i-1," ",c[i])) \\ _M. F. Hasler_, Oct 13 2009
%o A030168 (PARI) { default(realprecision, 2100); x=0.0; m=0; forprime (p=2, 4000, n=1+floor(log(p)/log(10)); x=p+x*10^n; m+=n; ); x=contfrac(x/10^m); for (n=1, 2001, write("b030168.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 30 2009
%Y A030168 Cf. A033308 (decimal expansion), A072754 (numerators of convergents), A072755 (denominators of convergents).
%K A030168 nonn,cofr,base
%O A030168 0,2
%A A030168 _Eric W. Weisstein_