The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A321221 Numbers of the form 6n-2 which are not a sum of two numbers that are the lesser of twin primes. 2
 4, 94, 400, 514, 784, 904, 1114, 1144, 1264, 1354, 3244, 4204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: This sequence is finite. If this sequence is finite, then the Goldbach Strong Conjecture is true. If p1 and p2 are the lesser of twin primes, then q1=p1+2 and q2=p2+2 are also primes (they are the greater of twin primes). If 6n-2 = p1+p2, then 6n = q1+p2 and 6n+2 = q1+q2. LINKS Marcin Barylski, On 6k ± 1 Primes in Goldbach Strong Conjecture Marcin Barylski, C++ program for generating A321221 EXAMPLE a(1) = 4 because 4 = 2+2; there are no other Goldbach partitions and 2 is not the lesser of twin primes. a(2) is not 6 because 6 = 3+3 and 3 is the lesser of twin primes. MATHEMATICA aQ[n_]:= (k=1; kmax=(n+2)/6; While[k<=kmax && !AllTrue[{6k-1, 6k+1, 6(kmax-k)-1, 6(kmax-k)+1}, PrimeQ], k++]; k>kmax); Select[6*Range[0, 10000]+4, aQ] (* Amiram Eldar, Nov 10 2018 *) PROG (PARI) ok(n)={if(n%6 == 4, forstep(k=3, n\2, 2, if(isprime(k) && isprime(k+2) && isprime(n-k) && isprime(n-k+2), return(0))); 1, 0)} \\ Andrew Howroyd, Nov 01 2018 CROSSREFS Cf. A001359, A002375. Sequence in context: A202899 A030246 A116160 * A116291 A061992 A221389 Adjacent sequences:  A321218 A321219 A321220 * A321222 A321223 A321224 KEYWORD nonn,more AUTHOR Marcin Barylski, Oct 31 2018 STATUS approved

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.

Last modified May 22 09:50 EDT 2022. Contains 353949 sequences. (Running on oeis4.)