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A033308 Decimal expansion of Copeland-Erdős constant: concatenate primes. 41
2, 3, 5, 7, 1, 1, 1, 3, 1, 7, 1, 9, 2, 3, 2, 9, 3, 1, 3, 7, 4, 1, 4, 3, 4, 7, 5, 3, 5, 9, 6, 1, 6, 7, 7, 1, 7, 3, 7, 9, 8, 3, 8, 9, 9, 7, 1, 0, 1, 1, 0, 3, 1, 0, 7, 1, 0, 9, 1, 1, 3, 1, 2, 7, 1, 3, 1, 1, 3, 7, 1, 3, 9, 1, 4, 9, 1, 5, 1, 1, 5, 7, 1, 6, 3, 1, 6, 7, 1, 7, 3, 1, 7, 9, 1, 8, 1, 1, 9, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The number .23571113171923.... was proved normal in base 10 by Copeland and Erdős but is not known to be normal in other bases. - Jeffrey Shallit, Mar 14 2008

REFERENCES

G. Harman, One hundred years of normal numbers, in M. A. Bennett et al., eds., Number Theory for the Millennium, II (Urbana, IL, 2000), 149-166, A K Peters, Natick, MA, 2002.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..2000

A. H. Copeland and P. Erdős, Note on Normal Numbers, Bull. Amer. Math. Soc. 52, 857-860, 1946.

Simon Plouffe, Copeland-Erdos constant, the primes concatenated

Simon Plouffe, Copeland-Erdos constant, the primes concatenated

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

FORMULA

Equals sum(n=1..inf, prime(n)*10^-A068670(n)). - Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006

Equals sum(i=1..inf, p_i * 10^-( sum(j=1..i, 1 + floor(log_10(p_j))) )) or sum(i=1..inf, p_i * 10^-( i + sum(j=1..i, floor(log_10(p_j))) )) or sum(i=1..inf, p_i * 10^-( sum(j=1..i, ceiling(log_10(1 + p_j))) )). - Daniel Forgues, Mar 26-28 2014

EXAMPLE

0.235711131719232931374143475359616771737983899710110310710911312...

MATHEMATICA

N[Sum[Prime[n]*10^-(n + Sum[Floor[Log[10, Prime[k]]], {k, 1, n}]), {n, 1, 40}], 100] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006 *)

N[Sum[Prime@n*10^-(n + Sum[Floor[Log[10, Prime@k]], {k, n}]), {n, 45}], 106] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006 *)

IntegerDigits //@ Prime@Range@45 // Flatten (* Robert G. Wilson v Oct 03 2006 *)

PROG

(PARI) default(realprecision, 2080); x=0.0; m=-1; forprime (p=2, 4000, n=1+floor(log(p)/log(10)); x=p+x*10^n; m+=n; ); x=x/10^m; for (n=0, 2000, d=floor(x); x=(x-d)*10; write("b033308.txt", n, " ", d)); \\ Harry J. Smith, Apr 30 2009

(Haskell)

a033308 n = a033308_list !! (n-1)

a033308_list = concatMap (map (read . return) . show) a000040_list :: [Int]

-- Reinhard Zumkeller, Mar 03 2014

CROSSREFS

Cf. A030168 (continued fraction).

Cf. A072754 (numerators of convergents), A072755 (denominators of convergents).

Cf. also A033307.

Cf. A000040, A165450, A019518.

Cf. A074721, A073034.

Sequence in context: A113493 A060420 A077648 * A134690 A228355 A065859

Adjacent sequences:  A033305 A033306 A033307 * A033309 A033310 A033311

KEYWORD

nonn,cons,base

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified September 22 14:19 EDT 2014. Contains 247065 sequences.