OFFSET
1,2
COMMENTS
a(n) is defined by the sign of the product sin(n*Pi/2) * sin(n*Pi/3) * sin(n*Pi/5) * sin(n*Pi/7) * sin(n*Pi/11), where Pi is A000796.
This construction assigns values a(p)=0 to the primes up to p-1 (here p=13), values a(p)=+1 to the primes from p to p^2-1, and zeros to all composites up to p^2-1.
The offset has been set to p to eliminate the leading zeros.
The "pseudo" in the name indicates that this kind of Fourier synthesis (or sieve) starts to fail at n=169=p^2: a(169)=1 although 169 is a composite number.
The extrema of the sine function are prime numbers, while the zeros are the composite numbers annihilated in the interval [p,p^2[.
A generalization is to use the sign of sin(n*Pi/2) *sin(n*Pi/3)*... *sin(n*Pi/p) for an even higher number of sine factors, which works to indicate correctly primes and composites in the interval n=p to p^2-1.
LINKS
Freimut Marschner and T. D. Noe, Table of n, a(n) for n = 1..1000 (249 terms from Freimut Marschner)
FORMULA
Numbers n such that sign(sin(n*Pi/2) * sin(n*Pi/3) * sin(n*Pi/5) * sin(n*Pi/7) * sin(n*Pi/11)) = 1.
MATHEMATICA
Select[Range[1000], Sign[Sin[#*Pi/2] * Sin[#*Pi/3] * Sin[#*Pi/5] * Sin[#*Pi/7] * Sin[#*Pi/11]] == 1 &] (* T. D. Noe, Aug 16 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Freimut Marschner, Aug 08 2013
STATUS
approved