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A129112
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Decimal expansion of constant equal to concatenated semiprimes.
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0
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4, 6, 9, 1, 0, 1, 4, 1, 5, 2, 1, 2, 2, 2, 5, 2, 6, 3, 3, 3, 4, 3, 5, 3, 8, 3, 9, 4, 6, 4, 9, 5, 1, 5, 5, 5, 7, 5, 8, 6, 2, 6, 5, 6, 9, 7, 4, 7, 7, 8, 2, 8, 5, 8, 6, 8, 7, 9, 1, 9, 3, 9, 4, 9, 5, 1, 0, 6, 1, 1, 1, 1, 1, 5, 1, 1, 8, 1, 1, 9, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 9
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OFFSET
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1,1
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COMMENTS
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Is this, as Copeland and Erdos (1946) showed for the Copeland-Erdos constant, a normal number in base 10? I conjecture that it is, despite the fact that the density of odd semiprimes exceeds the density of even semiprimes. What are the first few digits of the continued fraction of this constant? What are the positions of the first occurrence of n in the continued fraction? What are the incrementally largest terms and at what positions do they occur?
Coincides up to n=15 with concatenation of A046368. - M. F. Hasler, Oct 01 2007
Indeed, a theorem of Copeland & Erdős proves that this constant is 10-normal. - Charles R Greathouse IV, Feb 06 2015
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LINKS
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EXAMPLE
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4.691014152122252633343538394649515557586265...
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MATHEMATICA
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Flatten[IntegerDigits/@Select[Range[200], PrimeOmega[#]==2&]] (* Harvey P. Dale, Jan 17 2012 *)
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PROG
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(PARI) print1(4); for(n=6, 129, if(bigomega(n)==2, d=digits(n); for(i=1, #d, print1(", "d[i])))) \\ Charles R Greathouse IV, Feb 06 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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