A129950 - OEIS

%I #20 Sep 12 2024 16:04:12

%S 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,

%T 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,

%U -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

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

%C Absolute values are the same as A010051.

%H Antti Karttunen, <a href="/A129950/b129950.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A129950/a129950.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(n) = 2*A164292(n) - A010051(n). - _Antti Karttunen_, Jan 03 2019

%t Array[If[PrimeQ@ #, If[Or[PrimeQ[# - 2], PrimeQ[# + 2]], 1, -1], 0] &, 100] (* _Michael De Vlieger_, Jan 03 2019 *)

%o (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))

%o t(x) = if(abs(istwin(x))==1||x==5,1,if(isprime(x),-1,0))

%o for(j=1,100,print1(t(j)","))

%o (PARI) a(n) = if(isprime(n), (-1)^(!isprime(n-2) && !isprime(n+2)), 0); \\ Typos corrected by _Antti Karttunen_, Jan 03 2019

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

%K sign

%O 1,1

%A _Cino Hilliard_, Jun 10 2007

%E Definition and a(67) corrected by _M. F. Hasler_, Jan 20 2012