A129950 Indicator function of twin primes: 1 if n is a twin prime member, 0 if not prime, -1 else (isolated prime or 2).

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

Offset: 1

Author

Cino Hilliard, Jun 10 2007

Keywords

• sign

Comments

Absolute values are the same as A010051.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A001097, A001359, A006512, A010051, A077800, A164292.

Programs

Mathematica

Array[If[PrimeQ@ #, If[Or[PrimeQ[# - 2], PrimeQ[# + 2]], 1, -1], 0] &, 100] (* Michael De Vlieger, Jan 03 2019 *)

PARI

istwin(n) = local(p1, p2); if(n==5,return(2));if(isprime(n),p1=n-2;p2=n+2; if(isprime(p1),return(1));if(isprime(p2),return(-1));return(0))
t(x) = if(abs(istwin(x))==1||x==5,1,if(isprime(x),-1,0))
for(j=1,100,print1(t(j)","))

PARI

a(n) = if(isprime(n), (-1)^(!isprime(n-2) && !isprime(n+2)), 0); \\ Typos corrected by Antti Karttunen, Jan 03 2019

Formula

a(n) = 2*A164292(n) - A010051(n). - Antti Karttunen, Jan 03 2019

Extensions

Definition and a(67) corrected by M. F. Hasler, Jan 20 2012