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Search: id:A033308
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| A033308 |
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Decimal expansion of Copeland-Erdos constant: concatenate primes. |
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+0
33
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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The number .23571113171923.... was proved normal in base 10 by Copeland and Erdos but is not known to be normal in other bases. - Jeffrey Shallit, Mar 14 2008
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REFERENCES
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Copeland, A. H. and Erdos, P. "Note on Normal Numbers." Bull. Amer. Math. Soc. 52, 857-860, 1946.
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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..2000
S. Plouffe, Copeland-Erdos constant, the primes concatenated
S. Plouffe, Copeland-Erdos constant, the primes concatenated
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a = Sum[Prime[n]*10^-A68670[n], {n, 1, Infinity}] - Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006
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EXAMPLE
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0.235711131719232931374143475359616771737983899710110310710911312...
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MATHEMATICA
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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 *)
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PROGRAM
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(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)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 30 2009]
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CROSSREFS
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Cf. A030168 (continued fraction).
Cf. A072754 (numerators of convergents), A072755 (denominators of convergents).
Cf. also A033307.
Sequence in context: A113493 A060420 A077648 this_sequence A134690 A065859 A117819
Adjacent sequences: A033305 A033306 A033307 this_sequence A033309 A033310 A033311
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KEYWORD
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nonn,cons
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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