A317597 - OEIS

%I #9 Sep 15 2018 15:52:56

%S 10,4,128,98,308,488,1118,3818,1928,2438,992,2642,5372,7426,9596,

%T 64838,54244,48002,22832,100768,103738,63274,194470,194428,128168,

%U 180596,986332,850712,1403372,880508,3619208,5960648,503222,4454768,2209532,3526958,4445372

%N a(n) is the smallest even number for which there are n prime numbers between a(n) and the largest prime number p such that a(n)-p is also a prime.

%e For n=0, 10 = 7 + 3 is the smallest even number such that there is no prime between 7 and 10, so a(0)=10;

%e for n=1, 4 = 2 + 2 is the smallest even number such that there is only one prime between 2 and 4, which is 3, so a(1)=4;

%e for n=2, 128 = 109 + 19, there are two primes between 109 and 128, which are 113 and 127, for which a(n)-p = 15 and 1 respectively, and both nonprime.  There is no smaller even number having exactly 2 such primes, so a(2)=128.

%t fa = {}; n = 2; efa = 0; While[efa < 37, n = n + 2; p = NextPrime[n];

%t ct = 0; While[p = NextPrime[p, -1]; ! PrimeQ[n - p], ct++];

%t While[ct > (Length[fa] - 2), AppendTo[fa, 0]];

%t If[fa[[ct + 1]] == 0, fa[[ct + 1]] = n];

%t While[fa[[efa + 1]] > 0, efa++]];Part[fa,1;;efa]

%Y Cf. A317595.

%K nonn

%O 0,1

%A _Lei Zhou_, Aug 01 2018