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A102913
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Take characteristic function of the semiprimes A001358, interpret it as a binary fraction and convert to a decimal fraction.
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1
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0, 4, 0, 5, 7, 3, 5, 0, 0, 2, 0, 1, 3, 9, 8, 0, 6, 8, 6, 7, 4, 3, 1, 1, 2, 6, 6, 4, 2, 3, 5, 3, 5, 7, 5, 0, 6, 9, 3, 6, 2, 7, 5, 8, 2, 1, 9, 4, 0, 0, 2, 3, 5, 8, 6, 0, 8, 3, 3, 4, 0, 6, 9, 4, 6, 3, 3, 3, 6, 2, 5, 2, 4, 7, 3, 5, 1, 3, 5, 1, 3, 9, 1, 0, 5, 4, 4, 2, 5, 2, 5, 8, 2, 3, 8, 0, 5, 8, 6, 4, 3, 3, 4, 5, 2
(list;
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refs;
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text;
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OFFSET
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0,2
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LINKS
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Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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The characteristic function of the semiprimes is the function f(n) = 1 iff n is semiprime, 0 otherwise. This begins, for n = 0, 1, 2, 3, ... f(n) = 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1... If we concatenate these bits and interpret them as the binary fraction 0.0000101001100011000001... (base 2) we have, expressed as a decimal fraction, 0.0405735002013980686743112664235357506936275821940023586083340694633362...
The characteristic function of A001358 is A064911 (for n >= 1, starting with 0, 0, 0, 1 ...). The binary constant here has an additional 0 after the binary point. - Georg Fischer, Aug 04 2021
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MATHEMATICA
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Semiprime[n_] := If[Plus @@ Last[ Transpose[ FactorInteger[n]]] == 2, 1, 0]; RealDigits[ FromDigits[{Table[ Semiprime[n], {n, 2, 350}], -2}, 2], 10, 111][[1]] (* Ed Pegg Jr *)
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CROSSREFS
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For the continued fraction form of the semiprime constant, see A102914. For the equivalent characteristic function for primes, see A010051; interpreted as a binary fraction see A051006; for the continued fraction form of that see A051007.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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