A109440 Even numbers k such that exactly half of the primes p with p <= k/2 give k-p also a prime.

2, 6, 8, 14, 16, 18, 20, 26, 30, 42, 108, 132, 234, 264, 288, 354, 504, 1920, 2010, 5040

Offset

1,1

Comments

Let k be an even integer. Let PrimeP be the set of prime partition points {p,q} such that p + q = k, p and q are prime and p <= q. Let CompP be the set of composite partition points {p,q} such that p + q = k, p is prime, q is composite and p <= q. Sequence gives value of k such that the size of the two sets PrimeP and CompP are equal.

Even numbers k such that 2*A045917(k/2) = A000720(k/2). - Andrew Howroyd, Jan 02 2020

Links

Table of n, a(n) for n=1..20.

Example

The number k = 30 is included because the two sets PrimeP={{7,23},{11,19},{13,17}} and CompP={{2,28},{3,27},{5,25}} have the same number of elements.

Prog

(PARI)
d(n)={my(s=0); forprime(p=2, n, s+=if(isprime(2*n-p), 1, -1)); s}
{ for(n=1, 10^4/2, if(d(n)==0, print1(2*n, ", "))) } \\ Andrew Howroyd, Jan 02 2020

Crossrefs

Cf. A000720, A045917, A109885.

Sequence in context: A074400 A264598 A165607 * A063242 A210984 A213364

Adjacent sequences: A109437 A109438 A109439 * A109441 A109442 A109443

Keyword

nonn,more

Author

Gilmar Rodriguez Pierluissi (gilmarlily(AT)yahoo.com), Aug 26 2005

Extensions

Name edited and a(13)-a(20) from Andrew Howroyd, Jan 02 2020

Status

approved