%I #12 Nov 25 2015 20:53:02

%S 10,16,22,27,28,35,36,40,46,51,52,57,58,65,66,70,77,78,82,87,88,94,95,

%T 96,100,106,112,121,122,123,124,125,126,130,135,136,145,146,147,148,

%U 155,156,161,162,166,171,172,177,178,187,188,189,190,196,206,207,208

%N Composite numbers that are greater than the average of their closest flanking primes.

%C Composite numbers that are nearer to the immediately next prime than to the immediately previous prime.

%C Members of this sequence are the numbers C, necessarily composite, such that I_n < C < P_n+1, where P_n is the n-th odd prime and I_n the interprime (A024675) between P_n and P_n+1.

%C Prime-free subsequence of A264719.

%H Chris Boyd, <a href="/A264721/b264721.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7) = 36 because 36 > (31 + 37)/2 = 34.

%t Select[Range@ 208, And[CompositeQ@ #, # > (Abs@ NextPrime[#, -1] + NextPrime@ #)/2] &] (* _Michael De Vlieger_, Nov 22 2015 *)

%o (PARI) test(n)= {if(n-precprime(n-1)>nextprime(n+1)-n&&n>2&&!isprime(n),return(1),return(0))}

%o for(i=1,200,if(test(i),print1(i,", ")))

%Y Cf. A264719, A264720, A264722.

%K nonn,easy

%O 1,1

%A _Chris Boyd_, Nov 21 2015