Copeland–Erdős constant: Difference between revisions
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Its [[continued fraction]] is |
Its [[continued fraction]] is |
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<math> |
<math>0 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{8+\,\cdots}}}</math> ({{OEIS2C|id=A030168}}) |
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In base 10, this is a [[normal number]], a fact proven by [[Arthur Herbert Copeland]] and [[Paul Erdős]] in 1946 (hence the name of the constant). |
In base 10, this is a [[normal number]], a fact proven by [[Arthur Herbert Copeland]] and [[Paul Erdős]] in 1946 (hence the name of the constant). |
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Revision as of 20:52, 22 May 2006
The Copeland-Erdős constant is the concatenation of "0." with the base 10 representations of the prime numbers in order. Its value is approximately
0.235711131719232931374143... (sequence A033308 in the OEIS)
The larger Smarandache-Wellin numbers approximate the value of this constant multiplied by the appropriate power of 10.
Its continued fraction is
In base 10, this is a normal number, a fact proven by Arthur Herbert Copeland and Paul Erdős in 1946 (hence the name of the constant).