A129951 Sum of characteristic function of twin primes < 10^n.

2, 5, -30, -411, -4698, -45824, -428661, -4000209, -37149512, -345401797, -3220550623, -30125571140, -282726877353, -2661820464144, -25135733453455, -238021558244735, -2259761800241599, -21505250733431118

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Formula

Let t(m) = 1 if m is a twin prime member, -1 if isolated prime or 0 if not prime. Then a(n) = Sum_{k=1..10^n} t(k). [Corrected by Amiram Eldar, Jun 30 2024]

a(n) = 4*A007508(n) - A006880(n) - 2. - Amiram Eldar, Jun 30 2024

Prog

(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(n) = if(abs(istwin(n))==1||n==5, 1, if(isprime(n), -1, 0));
for(j=1, 10, print1(sum(x=1, 10^j, t(x))", "));

Crossrefs

Cf. A001097, A006880, A007508, A007510.

Sequence in context: A366455 A140786 A369726 * A127298 A275255 A219273

Adjacent sequences: A129948 A129949 A129950 * A129952 A129953 A129954

Keyword

sign,more

Author

Cino Hilliard, Jun 10 2007

Extensions

a(8)-a(18) from Amiram Eldar, Jun 30 2024

Status

approved