A102913 Take characteristic function of the semiprimes A001358, interpret it as a binary fraction and convert to a decimal fraction.

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

Author

Jonathan Vos Post, Jan 17 2005

Keywords

• cons
• nonn

Links

• Eric Weisstein's World of Mathematics, Prime Constant.
• Eric Weisstein's World of Mathematics, Semiprime.
• Eric Weisstein et al., Characteristic Function.

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.

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

Programs

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 *)

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

Extensions

More terms from Robert G. Wilson v, Jan 24 2005