The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109440 Even numbers k such that exactly half of the primes p with p <= k/2 give k-p also a prime. 0
2, 6, 8, 14, 16, 18, 20, 26, 30, 42, 108, 132, 234, 264, 288, 354, 504, 1920, 2010, 5040 (list; graph; refs; listen; history; text; internal format)



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


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


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.



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


Cf. A000720, A045917, A109885.

Sequence in context: A074400 A264598 A165607 * A063242 A210984 A213364

Adjacent sequences: A109437 A109438 A109439 * A109441 A109442 A109443




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


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)