A106667 a(n) = 1 if prime(n) + 2 is a prime, a(n) = -1 if prime(n) + 2 is a semiprime, otherwise 0.

-1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 0, -1, -1, 1, 0, -1, 1, 0, 0, -1, -1, 0, 1, 0, 1, -1, -1, -1, -1, 1, -1, 1, 0, -1, 0, -1, 0, 1, -1, 1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 0, -1, -1, -1, 1, 0, 0, 1, 0, -1, -1, 1, 0, -1, 0, -1, 1, 0, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, 1, 0, 1, 0, 0, -1, -1, 0, 1, 0, -1, -1, -1, -1

Offset: 1

Author

Giovanni Teofilatto, May 13 2005

Keywords

• easy
• sign
• less

Examples

			a(1) = -1 because prime(1) = 2 and 2 + 2 = 4 is a semiprime;
a(2) = 1 because prime(2) = 3 and 3 + 2 = 5 is a prime;
a(14) = 0 because prime(14) = 43 and 43 + 2 = 45 is neither prime nor semiprime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A063637.

Programs

Maple

p:= 1:
for n from 1 to 100 do
  p:= nextprime(p);
  if isprime(p+2) then A[n]:=1
  elif numtheory:-bigomega(p+2)=2 then A[n]:=-1
  else A[n]:= 0
  fi
od:
seq(A[n],n=1..100); # Robert Israel, Aug 29 2018

Extensions

Corrected, and definition clarified, by Robert Israel, Aug 29 2018