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

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, 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, 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

Offset

0,2

Links

M. F. Hasler, Table of n, a(n) for n = 0..5000

G. Xiao, Contfrac

Eric Weisstein's World of Mathematics, Copeland-Erdős Constant

Index entries for continued fractions for constants

Example

0.23571113171923293137414347... = 0 + 1/(4 + 1/(4 + 1/(8 + 1/(16 + ...))))

Mathematica

Take[ ContinuedFraction@ FromDigits[{Flatten[ IntegerDigits[ Prime@Range@ 47]], 0}], 95] (* Robert G. Wilson v, Oct 17 2013 *)

Prog

(PARI)
s=concat(vector(2000, i, Str(prime(i)))); c=contfrac(eval(s)/10^#s);
c2=contfrac((eval(s)+10^9)/10^#s);
for(i=1, #c, c[i]!=c2[i] & return(Str("Terms may be wrong for n>="i-1));
write("b030168.txt", i-1, " ", c[i])) \\ M. F. Hasler, Oct 13 2009
(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

Crossrefs

Cf. A033308 (decimal expansion), A072754 (numerators of convergents), A072755 (denominators of convergents).

Sequence in context: A095294 A190100 A244421 * A261212 A112435 A232508

Adjacent sequences: A030165 A030166 A030167 * A030169 A030170 A030171

Keyword

nonn,cofr,base

Author

Eric W. Weisstein

Status

approved