A102913 - OEIS

%I #17 Aug 04 2021 21:02:50

%S 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,

%T 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,

%U 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

%N Take characteristic function of the semiprimes A001358, interpret it as a binary fraction and convert to a decimal fraction.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstant.html">Prime Constant</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>.

%H Eric Weisstein et al., <a href="http://mathworld.wolfram.com/CharacteristicFunction.html">Characteristic Function</a>.

%F 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...

%F 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

%t 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_ *)

%Y 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.

%Y Cf. A001358, A010051, A051006, A064911, A102914.

%K cons,nonn

%O 0,2

%A _Jonathan Vos Post_, Jan 17 2005

%E More terms from _Robert G. Wilson v_, Jan 24 2005