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A102913
Take characteristic function of the semiprimes A001358, interpret it as a binary fraction and convert to a decimal fraction.
1
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
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Prime Constant.
Eric Weisstein's World of Mathematics, Semiprime.
Eric Weisstein et al., Characteristic Function.
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
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.
Sequence in context: A264757 A195773 A153018 * A197509 A180309 A102293
KEYWORD
cons,nonn
AUTHOR
Jonathan Vos Post, Jan 17 2005
EXTENSIONS
More terms from Robert G. Wilson v, Jan 24 2005
STATUS
approved